Equipotential Surfaces (15 Questions)

1. A charge of +10μC is placed at the origin. At what distance from the charge is the
potential 100V?
a) 0.09 m
b) 0.15 m
c) 0.1 m
d) 0.12 m
Answer: c) 0.1m
2. A point charge +2μC is placed at the center of a spherical shell of radius 0.2m.
What is the potential at the surface of the shell?
a) 90,000V
b) 45,000V
c) 18,000V
d) 36,000V
Answer: b) 45,000V
3. The work done in moving a charge q=2μC from x=0 to x=2m on an equipotential
surface is:
a) 0J
b) 100μJ
c) 50μJ
d) 200μJ
Answer: a) 0J
4. An equipotential surface is spherical for a point charge. What happens to the
potential as the radius increases?
a) Increases linearly
b) Decreases linearly
c) Decreases inversely with distance
d) Remains constant
Answer: c) Decreases inversely with distance
5. The potential difference between two points separated by 0.1m in a uniform electric
field of 200V/m is:
a) 20V
b) 200V
c) 10V
d) 40V
Answer: a) 20V
6. A charge +q is placed at the origin. What is the potential at a distance r=0.2m if
q=5μC?
a) 225,000V
b) 90,000V
c) 100,000V
d) 180,000V
Answer: a) 225,000V
7. The electric field at the surface of a conductor is perpendicular because:
a) Charges are stationary
b) Potential is zero
c) Surface is an equipotential
d) All of the above
Answer: c) Surface is an equipotential
8. At what distance from a 10μC charge is the potential 500V?
a) 0.18m
b) 0.2m
c) 0.15m
d) 0.25m
Answer: c) 0.2m
9. A sphere of radius 0.1m is an equipotential surface with potential 10V. The electric
field just outside the sphere is:
a) 10V/m
b) 100V/m
c) 0V/m
d) 1,000V/m
Answer: b) 100V/m
10. The potential of a 5μC charge at a distance 0.5m is:
a) 90,000V
b) 36,000V
c) 45,000V
d) 18,000V
Answer: c) 90,000V
11. Two charges of +3μC and +3μC are separated by 0.5m. At what point along
the line joining the charges is the potential zero?
a) At 0.25m from either charge
b) At 0.5m from either charge
c) No point exists
d) At infinity
Answer: c) No point exists
12. The electric field strength E is constant between two parallel plates with a
potential difference of V=50V and separation d=0.1m. What is E?
a) 250V/m
b) 500V/m
c) 100V/m
d) 50V/m
Answer: b) 500V/m
13. A charge +2μC is placed at the center of a spherical shell of radius 0.3m.
What is the potential at a point on the shell?
a) 60,000V
b) 40,000V
 c) 30,000V
d) 20,000V
Answer: a) 60,000V
14. The potential at a point due to a point charge is 500V. If the charge is
doubled, the potential at the same point will be:
a) 250V
b) 1,000V
c) 750V
d) 500V
Answer: b) 1,000V
15. A uniform electric field of 200V/m is directed along the x-axis. The potential
difference between two points separated by 0.05m along the x-axis is:
a) 5V
b) 10V
c) 20V
d) 25V
Answer: b) 10V

Electric Dipole (15 Questions)

11. Two charges +3μC and −3μC are separated by 0.2m. Find the dipole
moment.
a) 6μC⋅m
b) 0.6μC⋅m
c) 0.03μC⋅m
d) 1.2μC⋅m
Answer: a) 6μC⋅m
12. An electric dipole is placed in a uniform electric field of E=200N/C. The dipole
moment is p=5μC⋅m. What is the torque experienced by the dipole if it is oriented at
90∘ to the field?
a) 1.0N⋅m
b) 2.0N⋅m
c) 0.5N⋅m
d) 10N⋅m
Answer: a) 1.0N⋅m
13. The electric potential at a point on the axial line of a dipole is 20V. What will
be the potential at the same distance on the equatorial line?
a) 10V
b) 0V
c) 20V
d) 40V
Answer: b) 0V
14. A dipole of moment p=3μC⋅m is placed in a field E=100N/C. What is the
potential energy of the dipole when it is aligned with the field?
a) 0J
b) −0.3μJ
c) 0.3μJ
d) 1.5μJ
Answer: b) −0.3μJ
15. A dipole is placed in a uniform electric field with its dipole moment making an
angle of 60∘ with the field. If the dipole moment is 4μC⋅m and E=300N/C, what is
the torque on the dipole?
a) 0.12N⋅m
b) 0.6N⋅m
c) 0.36N⋅m
d) 1.2N⋅m
Answer: c) 0.36N⋅m
16. On the equatorial line of a dipole, the electric field is inversely proportional to:
a) r3
b) r2
c) r4
d) r5
Answer: a) r3
17. A dipole with a moment p=2μC⋅m is placed in a uniform field. It rotates from
90∘ to 0∘. The work done is:
a) 0.2μJ
b) 0.4μJ
c) 0.6μJ
d) 1.0μJ
Answer: b) 0.4μJ
 A dipole is oriented along the electric field. What is the net force acting on it?
a) pE
b) p/E
c) Zero
d) p⋅E2
Answer: c) Zero
 The electric field at a point on the axial line of a dipole is:
a) Zero
b) Proportional to p/r2
c) Proportional to p/r3
d) Proportional to 1/r2
Answer: c) Proportional to p/r3
 The torque on an electric dipole is maximum when the angle between dipole
moment and electric field is:
a) 0∘
 b) 45∘
c) 90∘
d) 180∘
Answer: c) 90∘

Analysis-Based MCQ Questions on Coulomb's Law (7 Questions)

1. If the force between two charges becomes 1/9th of its initial value, what is the
change in the distance between them?
a) Doubled
b) Tripled
c) Halved
d) Reduced to 1/3
Answer: b) Tripled
2. Two charges q1=5μC and q2=−5μC are separated by 0.4m. Analyze and calculate
the force between them.
a) 0.56N
b) 0.28N
c) 1.12N
d) Zero
Answer: a) 0.56N
3. Assertion-Reasoning:
Assertion: Coulomb’s force is a central force.
Reason: It acts along the line joining the two charges.
a) Both assertion and reason are true, and reason is the correct explanation of
assertion.
b) Both assertion and reason are true, but reason is not the correct explanation of
assertion.
c) Assertion is true, but reason is false.
d) Assertion is false, but reason is true.
Answer: a) Both assertion and reason are true, and reason is the correct
explanation of assertion.
4. How does the medium between two charges affect the Coulomb force?
a) Increases it
b) Decreases it based on the dielectric constant
c) Has no effect
d) Only changes the direction of the force
Answer: b) Decreases it based on the dielectric constant
5. Analyze the stability of a system of charges +q,−q,+q placed linearly with equal
spacing.
a) Stable due to symmetry
b) Unstable as like charges repel
c) Partially stable only for certain distances
d) Indeterminate
Answer: b) Unstable as like charges repel
6. Two charged spheres of equal radius have charges +2q and −q. If they are brought
into contact and separated, what will be the charge on each sphere?
a) +q and +q
b) +q and −q
c) +q/2 and −q/2
d) +q/2 and +q/2
Answer: a) +q and +q
7. A charge +q is placed at the center of a cube. Analyze the flux through one face of
the cube.
a) q/ϵ0
b) q/(6ϵ0)
c) q/(8ϵ0)
d) Zero
Answer: b) q/(6ϵ0)
 A charge q=5μC is placed inside a spherical shell. What is the total electric flux
through the shell?
a) 5.65×105N⋅m2/C
b) 1.13×106N⋅m2/C
c) Zero
d) Indeterminate
Answer: b) 1.13×106N⋅m2/C
 A large plane sheet has a uniform charge density σ=2μC/m2. What is the electric
field near the surface of the sheet?
a) 1.13×105N/C
b) 2.26×105N/C
c) 4.52×105N/C
d) Zero
Answer: b) 2.26×105N/C
 What is the electric field outside a spherical shell carrying a charge Q?
a) Zero
b) kQ/r2
c) kQ/r3
d) Proportional to 1/r4
Answer: b) kQ/r2
 A point charge q=5μC is placed inside a spherical shell. What is the total
electric flux through the shell?
a) 5.65×105N⋅m2/C
b) 1.13×106N⋅m2/C
c) Zero
d) Indeterminate
Answer: b) 1.13×106N⋅m2/C
 A spherical shell of radius R carries a uniform charge Q. What is the electric
field at a distance r=R/2 inside the shell?
 a) kQ/r2
b) Zero
c) Proportional to r3
d) Indeterminate
Answer: b) Zero
 What is the electric field outside a spherical shell of radius R carrying a
charge Q at a distance r=2R?
a) kQ/4R2
b) kQ/R2
c) 2kQ/R2
d) Zero
Answer: a) kQ/4R2
 A line charge with linear charge density λ=3μC/m is surrounded by a
cylindrical Gaussian surface of radius r=0.2m and length L=1m. What is the
total electric flux through the cylindrical surface?
a) 1.7×105N⋅m2/C
b) 3.4×105N⋅m2/C
c) 6.8×105N⋅m2/C
d) Zero
Answer: b) 3.4×105N⋅m2/C
 A uniformly charged sphere of radius R=0.5m has total charge Q=4μC. What
is the electric field at a point r=0.3m inside the sphere?
a) 1.2×105N/C
b) 1.08×105N/C
c) 0.48×105N/C
d) Zero
Answer: b) 1.08×105N/C
 A large plane sheet has a uniform charge density σ=2μC/m2. What is the
electric field near the surface of the sheet?
a) 1.13×105N/C
b) 2.26×105N/C
c) 4.52×105N/C
d) Zero
Answer: b) 2.26×105N/C
 A charge +q is placed at the center of a cube. Analyze the flux through one
face of the cube.
a) q/ϵ0
b) q/(6ϵ0)
c) q/(8ϵ0)
d) Zero
Answer: b) q/(6ϵ0)
 A solid sphere of radius R=0.2m has a charge density ρ=5μC/m3. What is the
electric field at r=R?
 a) 2.82×104N/C
b) 1.41×104N/C
c) 5.64×104N/C
d) Zero
Answer: a) 2.82×104N/C
 A charge is uniformly distributed over a sphere. What is the electric flux
through a concentric spherical Gaussian surface of radius r, where r>R?
a) q/ϵ0
b) 0
c) Proportional to 1/r2
d) None of the above
Answer: a) q/ϵ0
 A spherical shell has inner radius R1 and outer radius R2. A charge Q is
uniformly distributed in the shell. What is the field at r=R1?
a) Zero
b) kQ/R12
c) kQ/(R22−R12)
d) Indeterminate
Answer: a) Zero
 A cube of side 0.5m encloses a charge q=2μC. What is the flux through one
face of the cube?
a) 3.76×104N⋅m2/C
b) 7.52×104N⋅m2/C
c) 1.88×104N⋅m2/C
d) Zero
Answer: a) 3.76×104N⋅m2/C
 A long straight wire has a charge density λ. What is the electric field at a
distance r from the wire?
a) kλ/r
b) λ/(2πϵ0r)
c) kλ/r2
d) Zero
Answer: b) λ/(2πϵ0r)
 A cylindrical Gaussian surface encloses a charge q=8μC. If the length of the
cylinder is L=1m and radius r=0.2m, what is the flux through the curved
surface?
a) 9.05×105N⋅m2/C
b) 1.81×106N⋅m2/C
c) Zero
d) None of the above
Answer: b) 1.81×106N⋅m2/C
 A point charge is placed outside a closed surface. What is the net electric flux
through the surface?
 a) Zero
b) Equal to q/ϵ0
c) Proportional to the charge's distance
d) Indeterminate
Answer: a) Zero

Diagram-Based MCQ Questions on Electric Dipole (5 Questions)

1. [Diagram: A dipole in a uniform electric field oriented at an angle θ]
The dipole in the diagram experiences a torque. If the dipole moment is p and the
electric field is E, the torque is given by:
a) pE
b) pEcosθ
c) pEsinθ
d) Zero
Answer: c) pEsinθ
2. [Diagram: A point charge placed equidistant from both poles of a dipole]
What is the net force experienced by the point charge due to the dipole?
a) F=0
b) F=k⋅q⋅p/r3
c) F=k⋅q/r2
d) Cannot be determined
Answer: a) F=0
3. [Diagram: Two dipoles aligned head-to-tail at a distance r]
The net force between the two dipoles is:
a) Attractive and proportional to 1/r4
b) Repulsive and proportional to 1/r3
c) Zero
d) Attractive and proportional to 1/r3
Answer: a) Attractive and proportional to 1/r4
4. [Diagram: An electric dipole rotated 90∘ from its equilibrium position in a
uniform field]
What type of energy change occurs if the dipole is released from this position?
a) Kinetic energy increases, potential energy decreases
b) Kinetic energy decreases, potential energy increases
c) Both kinetic and potential energies increase
d) Both kinetic and potential energies decrease
Answer: a) Kinetic energy increases, potential energy decreases
5. [Diagram: A dipole placed near a conducting spherical shell with charges
distributed on it]
The dipole is attracted to the spherical shell. What is the reason?
a) Induced charges on the shell
b) Uniform distribution of charge
c) Repulsion between like charges
 d) Movement of charges inside the dipole
Answer: a) Induced charges on the shell

System of Charges: Numerical MCQs

1. Two charges q1=2μC and q2=−3μC are placed 4 m apart. What is the force
between them?
a) 1.35N (Attractive)
b) 1.35N (Repulsive)
c) 2.70N (Attractive)
d) 2.70N (Repulsive)
Answer: a) 1.35N (Attractive)
Solution: F=k⋅∣q1⋅q2∣/r2=9×109⋅2⋅10−6⋅3⋅10−6/42=1.35N.
2. Three charges q1=2μC, q2=2μC, and q3=−2μC are placed at the vertices of an
equilateral triangle of side 0.5m. What is the net force on q1?
a) 2.49N
b) 1.77N
c) 0.89N
d) 3.54N
Answer: a) 2.49N
3. Two charges of +10μC and −10μC are separated by 2m. What is the electric
field at the midpoint?
a) Zero
b) 4.5×105N/C
c) 9.0×105N/C
d) None of these
Answer: c) 9.0×105N/C
4. What is the potential energy of a system of two charges q1=5μC and q2=−5μC
separated by 0.3m?
a) −0.75J
b) −1.5J
c) 0.75J
d) 1.5J
Answer: a) −0.75J
Solution: U=k⋅q1⋅q2/r=9×109⋅5⋅10−6⋅(−5⋅10−6)/0.3=−0.75J.
5. Four charges, each of magnitude +2μC, are placed at the corners of a square
of side 2m. What is the net force on one of the charges?
a) 9N
b) 4.5N
c) 6.36N
d) 7.2N
Answer: d) 7.2N
 Two charges of q1=1μC and q2=4μC are separated by 1.5m. Where should a
third charge q3 be placed so that it experiences zero net force?
a) 0.5m from q1
b) 1.0m from q1
c) 0.75m from q1
d) 1.25m from q1
Answer: a) 0.5m from q1
 Two charges of q1=3μC and q2=−3μC are placed 1m apart. What is the electric
potential energy of the system?
a) −27J
b) −81J
c) −8.1J
d) None of these
Answer: a) −27J
 Two charges +q and −q are placed at points +a and −a on the x-axis. What is
the dipole moment?
a) 2qa
b) qa
c) −2qa
d) Zero
Answer: a) 2qa
 Three charges +2μC, −2μC, and +2μC are placed at the vertices of a triangle.
The side length is 1m. Find the net potential energy.
a) −0.18J
b) −0.36J
c) 0.18J
d) 0.36J
Answer: b) −0.36J
 Two charges q1=2μC and q2=−2μC are separated by 1m. Find the electric field
at the midpoint.
a) 36kN/C
b) 72kN/C
c) 144kN/C
d) Zero
Answer: c) 144kN/C
 Two charges q1=5μC and q2=5μC are separated by 3m. What is the potential
at the midpoint?
a) 15kV
b) 30kV
c) 45kV
d) Zero
Answer: b) 30kV
  Two charges +q and +2q are placed 1.2m apart. What is the force between
them?
a) 0.15N
b) 0.30N
c) 0.45N
d) None of these
Answer: c) 0.45N
Four charges of equal magnitude are placed at the corners of a square. The
magnitude of the force on any charge is proportional to:
a) 1/r2
b) 1/r
c) r2
d) Zero
Answer: a) 1/r2