Two point charges of +2 μC and -2 μC are placed 10 cm apart. What is the electric field at a point midway between them?
Answer: A
For a dipole configuration, the electric field at the midpoint is E = 2kq/r² directed from negative to positive charge. E = 2 × 9 × 10⁹ × 2 × 10⁻⁶ / (0.05)² = 7.2 × 10⁶ N/C
Q.2Easy
The electric potential due to a point charge is V = kq/r. If the charge is doubled and distance is halved, the potential becomes:
Answer: B
V' = k(2q)/(r/2) = 4kq/r = 4V. Doubling charge increases V by 2×, halving distance increases V by 2×, total effect is 4×
Q.3Easy
A conducting sphere of radius 10 cm carries a charge of 5 μC. The electric field at a distance of 5 cm from the center inside the conductor is:
Answer: A
Inside a conductor in electrostatic equilibrium, the electric field is always zero regardless of position or charge distribution
Q.4Easy
A parallel plate capacitor has plates of area A separated by distance d. If a dielectric of constant K is inserted between the plates, the capacitance becomes:
Answer: B
Capacitance with dielectric: C = Kε₀A/d, where K is the dielectric constant. The dielectric increases capacitance by a factor of K
Q.5Easy
The electric flux through a closed surface enclosing a net charge of 10 μC is:
An electric dipole with dipole moment p is placed in uniform electric field E at angle θ to the field. The torque on dipole is:
Answer: A
Torque on dipole in uniform field: τ = p × E = pE sinθ, where θ is angle between dipole moment and field
Q.7Easy
Two identical conducting spheres carry charges Q₁ and Q₂. They are brought in contact and then separated. The final charge on each sphere is:
Answer: A
When identical conducting spheres touch, charge distributes equally. Final charge on each = (Q₁ + Q₂)/2 by charge conservation
Q.8Easy
The electric field inside a uniformly charged spherical shell of radius R and charge Q at a distance r from center (r < R) is:
Answer: B
By Gauss's law, electric field inside a uniformly charged spherical shell is zero everywhere
Q.9Easy
A uniformly charged infinite plane sheet has surface charge density σ. What is the electric field at a distance d from the sheet?
Answer: A
For an infinite uniformly charged plane sheet, using Gauss's law with a cylindrical Gaussian surface, E = σ/(2ε₀), independent of distance.
Q.10Easy
A point charge q is enclosed by a closed surface. If the surface is deformed without changing the charge enclosed, the electric flux through the surface:
Answer: A
By Gauss's law, flux = Q/ε₀, independent of surface shape. Only the enclosed charge matters.
Q.11Easy
An electron is projected horizontally with velocity v into a uniform electric field E pointing downward. Its trajectory is:
Answer: A
Horizontal velocity constant, vertical acceleration due to E-field. Motion similar to projectile motion, hence parabolic.
Q.12Easy
A uniformly charged sphere of radius R and total charge Q has its charge density reduced by half. The electric potential at the surface becomes:
Answer: A
Surface potential V = kQ/R. If charge becomes Q/2, then V becomes kQ/(2R), which is half the original.
Q.13Easy
An electric dipole experiences maximum torque when placed in a uniform electric field at angle θ with respect to the field. The value of θ is:
Answer: C
Torque τ = pE sin(θ). Maximum when sin(θ) = 1, i.e., θ = 90°
Q.14Easy
A test charge q is moved from point A to point B in an electric field. The work done by the field is 100 J. If the same charge is moved from B to A, the work done is:
Answer: A
Electric force is conservative. Work done in reverse path = negative of original work. W(B→A) = -100 J
Q.15Easy
A uniformly charged infinite plane sheet has surface charge density σ. What is the electric field at a distance from the sheet?
Answer: A
For an infinite uniformly charged plane sheet, using Gauss's law with a cylindrical Gaussian surface, the electric field is E = σ/(2ε₀), independent of distance from the sheet.
Q.16Easy
An electric dipole with dipole moment p is placed in a non-uniform electric field. Which statement is correct?
Answer: C
In a non-uniform electric field, a dipole experiences both: (1) a torque due to the field trying to align it, and (2) a net force because the fields at the two ends are different.
Q.17Easy
The potential at distance r from a point charge Q is V. If the distance is doubled, the new potential is:
Answer: A
Electric potential V = kQ/r is inversely proportional to distance. If r → 2r, then V → V/2.
Q.18Easy
A charged particle enters a uniform electric field perpendicularly. Its path is:
Answer: B
Similar to projectile motion, a charged particle in a perpendicular electric field experiences constant acceleration, resulting in a parabolic trajectory.
Q.19Easy
What is the capacitance of an isolated conducting sphere of radius R in vacuum?
Answer: A
The capacitance of an isolated conducting sphere is C = 4πε₀R = R/k, where k = 1/(4πε₀).
Q.20Easy
The energy stored in a capacitor of capacitance C charged to potential V is:
Answer: B
Energy stored in a capacitor is U = (21)CV² = (21)QV = Q²/(2C).
