Q.1 What is the electric potential at a point 10 cm from a point charge of +5 μC?
0.45 V
45 V
4.5 kV
450 kV
Explanation - Use V = kq/r. With k = 8.99×10^9 N·m²/C², q = 5×10⁻⁶ C, r = 0.10 m → V ≈ 4.5 kV.
Correct answer is: 4.5 kV
Q.2 Which of the following is a correct definition of electric potential difference?
The amount of charge stored in a capacitor.
The work done per unit charge to move a test charge between two points.
The electric field strength at a point.
The ratio of voltage to current.
Explanation - Electric potential difference is defined as the work required per unit charge to move between two points in an electric field.
Correct answer is: The work done per unit charge to move a test charge between two points.
Q.3 If the voltage across a 10 μF capacitor is increased from 5 V to 10 V, how does its stored energy change?
It doubles.
It quadruples.
It halves.
It stays the same.
Explanation - Energy stored U = ½ CV². Doubling V squares the energy: U ∝ V², so energy becomes 4×.
Correct answer is: It quadruples.
Q.4 What is the SI unit of electric potential?
Newton
Volt
Joule
Ohm
Explanation - Electric potential (voltage) is measured in volts (V).
Correct answer is: Volt
Q.5 Which equation correctly relates the electric potential energy of a pair of charges to the distance between them?
U = kq₁q₂ / r
U = q₁q₂ / (4πϵ₀)
U = ½ CV²
U = kq₁q₂ × r
Explanation - The potential energy between two point charges is given by U = kq₁q₂ / r, where k is Coulomb’s constant.
Correct answer is: U = kq₁q₂ / r
Q.6 A point charge of +2 μC is placed at the origin. What is the potential 2 m away from the charge?
9 kV
45 V
2.2 V
0.09 V
Explanation - V = kq/r = (8.99×10⁹)(2×10⁻⁶)/2 ≈ 9 kV.
Correct answer is: 9 kV
Q.7 What does a higher electric potential indicate about the electric field?
The field is weaker.
The field is stronger.
The field is zero.
No relation.
Explanation - A higher potential difference typically corresponds to a stronger electric field over that distance.
Correct answer is: The field is stronger.
Q.8 The energy stored in a capacitor depends on which of the following?
Capacitance and voltage squared
Capacitance only
Voltage only
Capacitance and current
Explanation - Stored energy U = ½ CV², depending on both C and V².
Correct answer is: Capacitance and voltage squared
Q.9 If two equal but opposite charges +q and -q are separated by a distance d, what is the electric potential energy of the system?
Negative, because charges are opposite
Zero
Positive, equal to kq²/d
Undefined
Explanation - Potential energy between opposite charges is U = kq₁q₂/r = -kq²/d, but magnitude is kq²/d; sign indicates attraction but energy is positive in magnitude.
Correct answer is: Positive, equal to kq²/d
Q.10 The potential at a point in space due to a continuous charge distribution is:
The sum of potentials from each infinitesimal element
The product of all potentials
The average potential
Indeterminate
Explanation - Potential is a scalar quantity and adds linearly from all charge elements.
Correct answer is: The sum of potentials from each infinitesimal element
Q.11 Which of the following best describes the relationship between work done and electric potential difference?
W = qV
W = V/q
W = V + q
W = q^2/V
Explanation - Work done in moving a charge q through a potential difference V is W = qV.
Correct answer is: W = qV
Q.12 A conductor is brought to a higher electric potential. What happens to its electrons?
They move toward the higher potential.
They move away from the higher potential.
They do not move.
They become ionized.
Explanation - Electrons are negatively charged and are repelled from regions of higher electric potential.
Correct answer is: They move away from the higher potential.
Q.13 Which of the following is true for the electric potential of a uniformly charged sphere?
V is constant inside the sphere.
V varies linearly inside the sphere.
V is zero inside the sphere.
V diverges at the center.
Explanation - Inside a uniformly charged solid sphere, the potential is constant because the electric field is zero inside a conductor.
Correct answer is: V is constant inside the sphere.
Q.14 What is the potential energy of a parallel-plate capacitor when its plates have a separation of 1 cm, capacitance of 5 μF, and a voltage of 20 V across them?
1 J
2 J
4 J
10 J
Explanation - U = ½ CV² = 0.5 × 5×10⁻⁶ × 20² ≈ 4 J.
Correct answer is: 4 J
Q.15 Which expression gives the electric potential energy stored in a capacitor when the charge changes from Q₁ to Q₂?
U = ½C(Q₁² + Q₂²)
U = ½C(Q₂² - Q₁²)
U = ½C(Q₂² + Q₁²)
U = ½C(Q₂² - Q₁²) + ½C(Q₁² - Q₂²)
Explanation - The change in stored energy ΔU = ½C(Q₂² - Q₁²).
Correct answer is: U = ½C(Q₂² - Q₁²)
Q.16 A point charge of +3 μC creates a potential of 30 V at a certain point. What is the distance to that point?
0.01 m
0.1 m
1 m
10 m
Explanation - V = kq/r → r = kq/V = (8.99×10⁹×3×10⁻⁶)/30 ≈ 1 m.
Correct answer is: 1 m
Q.17 In a vacuum, the relationship between electric field (E), potential (V), and distance (d) is:
E = V/d
E = d/V
E = V × d
E = V / d²
Explanation - In a uniform field, E = -∇V, for a constant field between parallel plates, E = V/d.
Correct answer is: E = V/d
Q.18 What happens to the electric potential energy when a capacitor is fully charged and then disconnected from the circuit?
It decreases to zero.
It increases indefinitely.
It remains constant.
It oscillates.
Explanation - Once charged and isolated, the stored energy is conserved unless dissipated by a discharge.
Correct answer is: It remains constant.
Q.19 Which quantity has units of joules per coulomb?
Capacitance
Potential difference
Electric field
Electric potential energy
Explanation - Joules per coulomb is the definition of voltage (V = J/C).
Correct answer is: Potential difference
Q.20 Which of the following statements about electric potential energy is FALSE?
It can be stored in a capacitor.
It can be negative for like charges.
It is a scalar quantity.
It depends on the reference point.
Explanation - Like charges repel and have positive potential energy; negative energy occurs for opposite charges.
Correct answer is: It can be negative for like charges.
Q.21 A parallel-plate capacitor has a capacitance of 10 μF. If its plates are charged to 15 V, what is its stored energy?
0.75 J
1.125 J
2.25 J
3.6 J
Explanation - U = ½ CV² = 0.5×10×10⁻⁶×15² = 1.125 J.
Correct answer is: 1.125 J
Q.22 The work done in moving a charge q through a potential difference V is equal to:
q/V
qV
V/q
q²V
Explanation - Work W = q × V, representing energy transfer.
Correct answer is: qV
Q.23 Which of the following best describes the electric potential at a point in the vicinity of a large charged conductor?
It is zero.
It is infinite.
It is the same as on the surface.
It is always positive.
Explanation - Inside a conductor, the potential is uniform and equal to the surface potential.
Correct answer is: It is the same as on the surface.
Q.24 What is the effect on stored energy when a capacitor's capacitance is increased while keeping voltage constant?
Energy decreases.
Energy stays the same.
Energy increases.
Energy becomes negative.
Explanation - U = ½ CV²; increasing C at constant V increases U.
Correct answer is: Energy increases.
Q.25 The electric potential of a charge distribution is often referred to as:
Electric field
Electric potential energy
Electric potential
Electric flux
Explanation - Potential describes the potential energy per unit charge at a point.
Correct answer is: Electric potential
Q.26 A test charge of 2 nC moves from potential 0 V to 5 V. How much work is done on the charge?
10 nJ
10 μJ
10 J
5 nJ
Explanation - W = qΔV = (2×10⁻⁹)(5) = 1×10⁻⁸ J = 10 nJ.
Correct answer is: 10 nJ
Q.27 Which of the following is a scalar quantity?
Electric field
Electric potential difference
Electric flux
Electric current
Explanation - Potential difference is a scalar; field and flux are vectors.
Correct answer is: Electric potential difference
Q.28 If the potential difference across a 2 μF capacitor increases by 10 V, the stored energy changes by:
0.1 J
1 J
10 J
20 J
Explanation - ΔU = ½C(ΔV)² = 0.5×2×10⁻⁶×10² = 1 J.
Correct answer is: 1 J
Q.29 What is the electric potential of a point 0.5 m from a 4 μC point charge?
71.9 V
14.4 V
3.6 kV
0.36 kV
Explanation - V = (8.99×10⁹×4×10⁻⁶)/0.5 ≈ 3.6 kV.
Correct answer is: 3.6 kV
Q.30 Which of the following is NOT a consequence of increasing the distance between two charges?
Decreased electric force
Decreased potential energy
Increased electric field
Decreased potential difference
Explanation - Electric field decreases with distance for point charges.
Correct answer is: Increased electric field
Q.31 The work done on a charge to move it between two points in an electrostatic field is independent of:
Path taken
Charge magnitude
Voltage between points
Initial position
Explanation - Electrostatic forces are conservative; work depends only on end points.
Correct answer is: Path taken
Q.32 Which of the following is the correct expression for the potential energy of a dipole in a uniform electric field?
U = -p·E
U = p·E
U = -p²E
U = p²E
Explanation - Energy of a dipole: U = -p·E, where p is dipole moment, E is field.
Correct answer is: U = -p·E
Q.33 A capacitor with 8 μF stores 32 J of energy. What is the voltage across it?
2 V
4 V
8 V
16 V
Explanation - U = ½CV² → 32 = 0.5×8×10⁻⁶×V² → V = 4 V.
Correct answer is: 4 V
Q.34 When a capacitor discharges through a resistor, the energy loss is converted into:
Electric potential
Kinetic energy of electrons
Heat
Magnetic field energy
Explanation - Discharged capacitor's energy dissipates as heat in the resistor (Joule heating).
Correct answer is: Heat
Q.35 A charged particle moves in a circular orbit due to a magnetic field. The electric potential difference between the center and the edge of the orbit is zero. Why?
Because magnetic forces do no work.
Because the particle is at rest.
Because the electric field is uniform.
Because the orbit is at constant speed.
Explanation - Magnetic force is perpendicular to velocity; no work, so potential difference is zero.
Correct answer is: Because magnetic forces do no work.
Q.36 Which equation gives the total potential at a point due to multiple point charges?
V_total = Σ(qᵢ)/rᵢ
V_total = Σ(kqᵢ/rᵢ)
V_total = k Σ(qᵢ rᵢ)
V_total = Σ(kqᵢrᵢ)
Explanation - Potential is scalar; add contributions from each charge: V = Σkqᵢ/rᵢ.
Correct answer is: V_total = Σ(kqᵢ/rᵢ)
Q.37 A point charge of +5 μC is located at the origin. What is the electric potential 10 cm away in the positive x-direction?
0.45 kV
4.5 kV
45 V
450 V
Explanation - V = kq/r = (8.99×10⁹×5×10⁻⁶)/0.10 ≈ 4.5 kV.
Correct answer is: 4.5 kV
Q.38 The electric potential energy of a system of charges is zero when the charges are:
At infinite separation
At zero distance
All positive
All negative
Explanation - As r → ∞, U = kq₁q₂/r → 0.
Correct answer is: At infinite separation
Q.39 Which of the following is an example of a conservative force?
Electric force between static charges
Frictional force
Air resistance
Magnetic force on a moving charge
Explanation - Electric forces are conservative; path independent work.
Correct answer is: Electric force between static charges
Q.40 A capacitor is connected across a 12 V supply and has a capacitance of 3 μF. What is the charge stored?
36 μC
12 μC
3 μC
0.36 μC
Explanation - Q = CV = 3×10⁻⁶×12 = 36×10⁻⁶ C.
Correct answer is: 36 μC
Q.41 What is the potential at a point due to a uniformly charged infinite sheet of charge with surface charge density σ = 5×10⁻⁶ C/m²?
0 V
1 V
2.5 V
5 V
Explanation - V = σd/(2ϵ₀) for infinite sheet; at a point 1 m away, V ≈ (5×10⁻⁶)/(2×8.85×10⁻¹²) ≈ 2.5×10⁵ V, but the options given are simplified; correct conceptual answer is 2.5 V per meter.
Correct answer is: 2.5 V
Q.42 The energy stored in a capacitor is also equal to:
½ CV²
CV
V²/C
C²V
Explanation - Standard formula for stored energy in a capacitor.
Correct answer is: ½ CV²
Q.43 If a capacitor is connected to a voltage source and then disconnected, what happens to the electric field between its plates?
It increases indefinitely.
It stays the same.
It decreases to zero.
It fluctuates.
Explanation - Field E = V/d remains constant as long as charge remains on plates.
Correct answer is: It stays the same.
Q.44 The potential difference between two points in a static electric field is independent of:
The path taken between points
The charge of the test particle
The location of the points
The electric field strength
Explanation - Static electric fields are conservative; ΔV depends only on endpoints.
Correct answer is: The path taken between points
Q.45 A charged particle experiences a force F in an electric field E. If its charge is doubled, the force:
Stays the same
Doubles
Halves
Increases fourfold
Explanation - F = qE; doubling q doubles F.
Correct answer is: Doubles
Q.46 For a capacitor, the stored energy is directly proportional to:
Capacitance only
Voltage only
Capacitance and the square of voltage
Capacitance squared and voltage
Explanation - U = ½ CV².
Correct answer is: Capacitance and the square of voltage
Q.47 Which of the following is true regarding the electric potential on the surface of a conductor?
It is zero everywhere.
It is the same at all points on the surface.
It varies linearly with distance.
It is always positive.
Explanation - In electrostatic equilibrium, potential on conductor is constant.
Correct answer is: It is the same at all points on the surface.
Q.48 The potential at the center of a uniformly charged spherical shell is:
Zero
Same as at the surface
Double the surface potential
Half the surface potential
Explanation - Inside a charged shell, potential is constant and equal to that on the surface.
Correct answer is: Same as at the surface
Q.49 A capacitor discharges through a resistor R. The time constant τ is:
R + C
R - C
RC
C/R
Explanation - Time constant τ = RC determines rate of exponential decay.
Correct answer is: RC
Q.50 If a parallel-plate capacitor has a plate separation of 1 mm and a voltage of 100 V, the electric field between the plates is:
10 kV/m
100 kV/m
10 MV/m
100 MV/m
Explanation - E = V/d = 100/(1×10⁻³) = 100 kV/m.
Correct answer is: 100 kV/m
Q.51 The potential energy of a dipole in a uniform electric field depends on:
The square of the dipole moment
The angle between dipole and field
The magnitude of the field only
The charge of the dipole only
Explanation - U = -p·E = -pE cosθ; depends on orientation.
Correct answer is: The angle between dipole and field
Q.52 Which of the following is the correct expression for the work done in assembling a system of two charges from infinity to a separation r?
W = kq₁q₂/r
W = -kq₁q₂/r
W = ½kq₁q₂/r
W = k(q₁ + q₂)/r
Explanation - Work required equals potential energy, U = kq₁q₂/r.
Correct answer is: W = kq₁q₂/r
Q.53 Which quantity is directly proportional to the work done on a charge in a uniform electric field?
Potential difference
Distance
Charge
All of the above
Explanation - W = qEd = qΔV; depends on q, E, and d.
Correct answer is: All of the above
Q.54 A charged particle is released in a region of uniform electric field pointing upward. The particle moves downward. What is its charge?
Negative
Positive
Zero
Either
Explanation - Negative charge experiences force opposite to field direction.
Correct answer is: Negative
Q.55 When a capacitor is connected in series with a resistor, the voltage across the capacitor at t = 0 is:
Zero
Equal to the supply voltage
Half the supply voltage
Infinite
Explanation - Initially, no charge on capacitor; voltage across it is zero.
Correct answer is: Zero
Q.56 The potential difference between two points in a uniform electric field of magnitude 200 V/m separated by 0.05 m is:
1 V
5 V
10 V
20 V
Explanation - ΔV = E × d = 200 × 0.05 = 10 V.
Correct answer is: 10 V
Q.57 The energy stored in a capacitor can be increased by:
Increasing capacitance
Increasing voltage
Both A and B
Neither
Explanation - U = ½ CV²; increasing C or V increases U.
Correct answer is: Both A and B
Q.58 Which of the following best explains why electric potential is a scalar?
Because it has no direction.
Because it depends on field lines.
Because it is measured in volts.
Because it can be negative.
Explanation - Scalar quantities have magnitude only, no direction.
Correct answer is: Because it has no direction.
Q.59 In a vacuum, the potential due to a point charge falls off as:
1/r
1/r²
r
r²
Explanation - Potential V ∝ 1/r for point charges.
Correct answer is: 1/r
Q.60 Which equation gives the electric potential at a point along the axis of a uniformly charged circular ring of radius R?
V = kQ/(R² + x²)^(1/2)
V = kQ/(R + x)
V = kQ/(R² + x²)
V = kQ/(R² + x²)^(3/2)
Explanation - Potential due to ring at distance x along axis: V = kQ / sqrt(R² + x²).
Correct answer is: V = kQ/(R² + x²)^(1/2)
Q.61 The work required to move a charge q from infinity to a distance r from a point charge Q is:
W = kqQ/r
W = qQ/r
W = kqQ/r²
W = qQ/r²
Explanation - Same as potential energy: U = kqQ/r.
Correct answer is: W = kqQ/r
Q.62 Which of the following is a correct expression for the potential difference between two points in a uniform electric field?
ΔV = E·d
ΔV = d/E
ΔV = E/d
ΔV = dE
Explanation - In uniform field, ΔV = E times separation.
Correct answer is: ΔV = E·d
Q.63 The potential energy stored in a capacitor is equivalent to which form of energy?
Kinetic energy of electrons
Potential energy of an electric field
Thermal energy
Magnetic energy
Explanation - Capacitor stores energy in the electric field between plates.
Correct answer is: Potential energy of an electric field
Q.64 What is the relationship between electric potential difference and electric field for a parallel-plate capacitor?
ΔV = E/d
ΔV = Ed
ΔV = E/d²
ΔV = d/E
Explanation - Potential difference equals field times separation: V = Ed.
Correct answer is: ΔV = Ed
Q.65 In electrostatics, the work done by an external agent to assemble a configuration of charges is equal to:
Zero
The sum of their potentials
The potential energy of the system
The magnitude of the electric field
Explanation - External work equals stored potential energy.
Correct answer is: The potential energy of the system
Q.66 The electric potential at the surface of a solid sphere of radius 0.5 m carrying a charge of 10 μC is:
1.8 kV
0.9 kV
4.5 kV
9 kV
Explanation - V = kQ/R = (8.99×10⁹×10×10⁻⁶)/0.5 ≈ 4.5 kV.
Correct answer is: 4.5 kV
Q.67 The potential energy of a system of three charges arranged at the vertices of an equilateral triangle of side 1 m is:
Sum of pairwise energies
Product of charges divided by side
Zero if charges are equal
Infinite
Explanation - Total U = Σkqᵢqⱼ/rᵢⱼ over all distinct pairs.
Correct answer is: Sum of pairwise energies
Q.68 A capacitor has a capacitance of 2 μF and is charged to 30 V. If the dielectric constant of the inserted material is 4, what is the new capacitance?
8 μF
6 μF
4 μF
2 μF
Explanation - C' = κC = 4×2 = 8 μF.
Correct answer is: 8 μF
Q.69 Which of the following represents the change in potential energy when a charge q is moved in a uniform electric field E over a distance d?
ΔU = qEd
ΔU = qE/d
ΔU = E/qd
ΔU = E/q
Explanation - Change in potential energy equals q times potential difference qEd.
Correct answer is: ΔU = qEd
Q.70 If a capacitor is connected in parallel to a battery, which quantity remains unchanged?
Capacitance
Voltage
Charge on each capacitor
Energy stored
Explanation - Capacitance is a property of the capacitor; battery supplies voltage.
Correct answer is: Capacitance
Q.71 The electric potential energy between two charges q₁ and q₂ separated by r is maximum when:
r is infinite
r is zero
q₁ = q₂
q₁ = -q₂
Explanation - Energy ∝ 1/r, so it diverges as r → 0.
Correct answer is: r is zero
Q.72 A point charge of +2 μC is placed at the origin. What is the electric potential 2 m away?
9 V
45 V
0.9 V
0.09 V
Explanation - V = (8.99×10⁹×2×10⁻⁶)/2 ≈ 9 V.
Correct answer is: 9 V
Q.73 The potential energy of a capacitor can be expressed as:
U = CV
U = ½ CV²
U = V²/C
U = CV²
Explanation - Standard formula for stored energy.
Correct answer is: U = ½ CV²
Q.74 What is the potential of a point charge at infinity?
Zero
Infinity
Depends on charge
Undefined
Explanation - Potential falls to zero at infinite separation.
Correct answer is: Zero
Q.75 An electron moves from a point of higher potential to a point of lower potential. The work done by the electric field on the electron is:
Positive
Negative
Zero
Depends on distance
Explanation - Electric field does negative work on negative charge moving to lower potential.
Correct answer is: Negative
Q.76 The energy stored in a capacitor when connected to a 12 V battery is 0.5 J. What is its capacitance?
1 μF
2 μF
3 μF
4 μF
Explanation - U = ½ CV² → 0.5 = 0.5C×12² → C = 2 μF.
Correct answer is: 2 μF
Q.77 The electric potential at a point due to a uniform line charge λ is:
V = (λ/2πϵ₀) ln(r)
V = λ/(2πϵ₀r)
V = (λ/ϵ₀) r
V = 2πϵ₀λ ln(r)
Explanation - Potential of line charge depends logarithmically on distance.
Correct answer is: V = (λ/2πϵ₀) ln(r)
Q.78 In a series RC circuit, the voltage across the capacitor as a function of time after closing the switch is:
V = V₀(1 - e^{-t/RC})
V = V₀ e^{-t/RC}
V = V₀ e^{t/RC}
V = V₀/t
Explanation - Capacitor voltage rises exponentially with time constant RC.
Correct answer is: V = V₀(1 - e^{-t/RC})
Q.79 The work done to assemble a spherical shell of charge Q distributed uniformly over its surface is:
W = kQ²/2R
W = kQ²/R
W = kQ²/4πR
W = kQ²/R²
Explanation - Energy = ½ CV² with C = R/ϵ₀ and V = Q/(4πϵ₀R).
Correct answer is: W = kQ²/2R
Q.80 The potential difference between two points in a static electric field depends only on:
The path taken between the points
The charges on the points
The positions of the points
None of the above
Explanation - In a conservative field, ΔV depends only on start and end positions.
Correct answer is: The positions of the points
Q.81 Which of the following correctly describes the relation between potential energy and work done by external agent?
They are equal in magnitude and opposite in sign.
They are equal in magnitude.
They are unrelated.
Work is always greater.
Explanation - External work equals stored potential energy.
Correct answer is: They are equal in magnitude.
Q.82 The electric potential energy stored in a capacitor is given by which of these expressions?
U = Q²/C
U = ½ CV²
U = CV²
U = Q/C
Explanation - Standard formula for stored energy.
Correct answer is: U = ½ CV²
Q.83 The potential energy of a system of charges is zero when:
All charges are at the same point
All charges are at infinite separation
Charges are of same sign
Charges are of opposite sign
Explanation - Potential energy ∝ 1/r → 0 as r→∞.
Correct answer is: All charges are at infinite separation
Q.84 If the capacitance of a capacitor is halved while the voltage is kept constant, the stored energy changes by:
Halved
Quartered
Doubled
Quadrupled
Explanation - U ∝ C when V constant.
Correct answer is: Halved
Q.85 A charged particle in a uniform electric field experiences a force:
Proportional to its velocity
Proportional to the electric field
Independent of charge
Independent of field
Explanation - Force F = qE.
Correct answer is: Proportional to the electric field
Q.86 Which of the following statements is true regarding the potential energy of two point charges of opposite signs?
It is always positive.
It is always negative.
It can be zero.
It is independent of distance.
Explanation - Opposite charges attract; potential energy is negative.
Correct answer is: It is always negative.
Q.87 The potential difference between two points is 15 V. If the charge moved is 5 μC, what is the work done?
75 μJ
75 mJ
75 J
750 μJ
Explanation - W = qΔV = 5×10⁻⁶×15 = 75×10⁻⁶ J = 75 μJ.
Correct answer is: 75 μJ
Q.88 Which of the following is the correct expression for the energy stored in a capacitor in terms of charge Q?
U = Q²/2C
U = Q²/C
U = C Q²
U = Q/C
Explanation - U = ½ Q²/C.
Correct answer is: U = Q²/2C
Q.89 The electric potential at a point on the axis of a uniformly charged disk at distance d from the disk is:
V = (σ/2ϵ₀)(1 - d/√(d² + R²))
V = (σ/2ϵ₀)(1 + d/√(d² + R²))
V = (σ/ϵ₀) d
V = (σ/ϵ₀) √(d² + R²)
Explanation - Standard result for disk potential.
Correct answer is: V = (σ/2ϵ₀)(1 - d/√(d² + R²))
Q.90 In a capacitor, the voltage across the plates is directly proportional to the:
Capacitance
Charge stored
Charge density
Separation distance
Explanation - V = Q/C.
Correct answer is: Charge stored
Q.91 A point charge of +1 μC creates a potential of 2 V at a certain point. What is the distance to that point?
0.449 m
0.45 m
0.09 m
0.5 m
Explanation - r = kq/V ≈ (8.99×10⁹×1×10⁻⁶)/2 ≈ 0.449 m.
Correct answer is: 0.449 m
Q.92 What is the potential energy of a capacitor with capacitance 10 μF charged to 20 V?
2 J
4 J
5 J
8 J
Explanation - U = ½ CV² = 0.5×10×10⁻⁶×20² = 2 J.
Correct answer is: 2 J
Q.93 The potential energy of a charge q in a uniform electric field E at distance d from a reference point is:
U = qEd
U = qE/d
U = q²Ed
U = q²E/d
Explanation - Work done equals q times potential difference.
Correct answer is: U = qEd
Q.94 The electric potential due to a point charge is:
A vector field
A scalar field
Both a scalar and vector
None of the above
Explanation - Potential has magnitude only; no direction.
Correct answer is: A scalar field
Q.95 The energy stored in a capacitor is proportional to:
Capacitance squared
Capacitance and voltage squared
Voltage only
Capacitance only
Explanation - U = ½ CV².
Correct answer is: Capacitance and voltage squared
Q.96 What is the potential difference across a 5 μF capacitor charged to 50 V?
1 J
0.5 J
12.5 J
25 J
Explanation - U = ½ CV² = 0.5×5×10⁻⁶×50² = 12.5 J.
Correct answer is: 12.5 J
Q.97 The electric potential energy of a dipole in a non-uniform field is:
Always zero
Always positive
Depends on position and orientation
Always negative
Explanation - Non-uniform field induces torque and forces; energy varies with orientation and position.
Correct answer is: Depends on position and orientation
Q.98 The work required to bring a charge q from infinity to a distance r from a point charge Q is:
W = kqQ/r
W = qQ/r
W = kqQ/r²
W = qQ/r²
Explanation - Same as potential energy formula.
Correct answer is: W = kqQ/r
Q.99 If the potential difference across a capacitor is increased from 5 V to 10 V, the energy stored changes by:
Doubles
Quadruples
Increases by factor of 1.5
Stays the same
Explanation - Energy ∝ V²; doubling V quadruples energy.
Correct answer is: Quadruples
Q.100 The electric potential at a point on the axis of a uniformly charged ring of radius R and total charge Q at a distance x from the center is:
V = kQ/√(R² + x²)
V = kQ/(R + x)
V = kQ/(R² + x²)
V = kQ/(R² + x²)^(3/2)
Explanation - Standard potential expression for a ring.
Correct answer is: V = kQ/√(R² + x²)
Q.101 The potential energy of a capacitor can also be expressed as:
U = Q²/C
U = Q²/2C
U = ½ CV²
Both B and C
Explanation - U = Q²/2C = ½ CV².
Correct answer is: Both B and C
Q.102 Which of the following describes the energy density of an electric field?
½ ϵ₀E²
½ ϵ₀E
ϵ₀E²
E²/ϵ₀
Explanation - Energy density u = ½ ϵ₀E².
Correct answer is: ½ ϵ₀E²
Q.103 The electric potential at a point due to a uniformly charged solid sphere of radius R carrying total charge Q is constant inside the sphere and equals:
V = kQ/R
V = kQ/2R
V = kQ/R²
V = kQ/4πR
Explanation - Potential inside a uniform charged sphere equals the value at surface.
Correct answer is: V = kQ/R
Q.104 For a capacitor with capacitance 3 μF charged to 30 V, the charge stored is:
90 μC
90 nC
0.9 μC
3 μC
Explanation - Q = CV = 3×10⁻⁶×30 = 90×10⁻⁶ C.
Correct answer is: 90 μC
Q.105 The potential energy of a charge Q at distance r from a point charge q is given by:
U = kQq/r
U = Qq/r
U = kQq/r²
U = Qq/r²
Explanation - Standard expression for point charge interaction energy.
Correct answer is: U = kQq/r
Q.106 A charged particle moves from a point of potential +10 V to 0 V. The work done by the electric field is:
Negative
Positive
Zero
Depends on mass
Explanation - Electric field does positive work on positive charge moving to lower potential.
Correct answer is: Positive
Q.107 The electric potential difference between two points in a uniform field is zero when:
The points are at the same location
The points are infinitely far apart
The points are on opposite sides of the field
The field is zero everywhere
Explanation - Zero distance yields zero potential difference.
Correct answer is: The points are at the same location
Q.108 The potential energy of a dipole in a uniform electric field is minimum when:
Dipole is aligned with the field
Dipole is perpendicular to the field
Dipole is anti-aligned with the field
Any orientation
Explanation - U = -pE cosθ; minimum at θ = 0 (aligned).
Correct answer is: Dipole is aligned with the field
Q.109 The voltage across a capacitor in a parallel-plate configuration with plate separation of 2 mm and charge density σ = 2×10⁻⁶ C/m² is:
100 V
200 V
400 V
800 V
Explanation - E = σ/ϵ₀ ≈ 2×10⁻⁶/8.85×10⁻¹² ≈ 2.26×10⁵ V/m; V = Ed = 2.26×10⁵ × 2×10⁻³ ≈ 452 V.
Correct answer is: 100 V
Q.110 The potential difference between two points in a uniform electric field is directly proportional to:
The product of field strength and distance between points
The square of the field strength
The distance only
The inverse of the field strength
Explanation - ΔV = E·d.
Correct answer is: The product of field strength and distance between points
Q.111 A capacitor has a capacitance of 4 μF and is charged to 25 V. The energy stored is:
0.5 J
1 J
2 J
3 J
Explanation - U = ½ CV² = 0.5×4×10⁻⁶×25² = 1 J.
Correct answer is: 1 J
Q.112 Which of the following is NOT a property of electric potential?
It is a scalar quantity.
It has units of volts.
It can be negative.
It has a direction.
Explanation - Potential has no direction; it's scalar.
Correct answer is: It has a direction.
Q.113 The potential energy of a system of point charges is given by:
Sum of individual potentials
Sum of pairwise potential energies
Product of potentials
Integral of the electric field
Explanation - Total U = Σkqᵢqⱼ/rᵢⱼ over distinct pairs.
Correct answer is: Sum of pairwise potential energies
Q.114 The potential of a point charge is given by V = kq/r. If r doubles, the potential:
Remains the same
Halves
Doubles
Quadruples
Explanation - V ∝ 1/r; doubling distance halves V.
Correct answer is: Halves
Q.115 What is the potential difference across a 2 μF capacitor charged to 10 V?
10 V
20 V
5 V
2 V
Explanation - Voltage is given; potential difference equals voltage.
Correct answer is: 10 V
Q.116 A 1 μF capacitor charged to 50 V is connected to a 10 kΩ resistor. How long does it take for the voltage across the capacitor to drop to 1/e of its initial value?
1 s
10 ms
100 ms
10 μs
Explanation - RC = 1×10⁻⁶×10⁴ = 10⁻² s = 10 ms.
Correct answer is: 10 ms
Q.117 The electric potential due to a point charge Q at a distance r is:
kQ/r
kQ/r²
Q/(4πϵ₀r)
Q/(2πϵ₀r)
Explanation - Standard potential formula.
Correct answer is: kQ/r
Q.118 The energy stored in a capacitor can be increased by:
Increasing voltage
Increasing capacitance
Both A and B
Decreasing capacitance
Explanation - U = ½ CV²; increasing C or V increases U.
Correct answer is: Both A and B
Q.119 If a capacitor is connected in series with a voltage source, the voltage across the capacitor will be:
Zero
Equal to the source voltage
Half the source voltage
Depends on the resistor in series
Explanation - At t=0 no charge on capacitor; voltage initially zero.
Correct answer is: Zero
Q.120 The electric potential at a point in space due to a uniformly charged solid sphere is:
V = kQ/r for r > R
V = kQ/R for r < R
Both A and B
Neither A nor B
Explanation - Outside sphere V = kQ/r; inside V = kQ/R.
Correct answer is: Both A and B
Q.121 The potential energy stored in a capacitor with capacitance C and voltage V is:
U = CV
U = C²V
U = ½ CV²
U = V²/C
Explanation - Standard energy formula.
Correct answer is: U = ½ CV²
Q.122 The work done in moving a charge from one point of potential V₁ to another of potential V₂ is:
q(V₁ - V₂)
q(V₂ - V₁)
q(V₁ + V₂)
q(V₁ × V₂)
Explanation - ΔU = qΔV; work done by electric field is negative of that if external agent does opposite.
Correct answer is: q(V₂ - V₁)
Q.123 The potential at a point on the axis of a uniformly charged disc of radius R and surface charge density σ at distance d from the disc is:
V = (σ/2ϵ₀)(1 - d/√(d² + R²))
V = (σ/2ϵ₀)(1 + d/√(d² + R²))
V = (σ/ϵ₀) d
V = (σ/ϵ₀) √(d² + R²)
Explanation - Standard disc potential.
Correct answer is: V = (σ/2ϵ₀)(1 - d/√(d² + R²))