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.222Medium
The electric field intensity at distance r from a line charge with linear charge density λ is given by:
Answer: B
Using Gauss's law with cylindrical surface: E × 2πr = λL/ε₀, hence E = λ/(2πε₀r)
Q.223Medium
A parallel plate capacitor has capacitance C and is charged to voltage V. If voltage is doubled and a dielectric K is inserted, the energy stored becomes:
Answer: A
U = ½C'V'² where C' = KC and V' = 2V. So U = ½(KC)(2V)² = 4CKV²
Q.224Easy
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.225Easy
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.
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Q.226Medium
A metallic sphere of radius R is charged such that surface charge density is σ. If the sphere is surrounded by a dielectric medium of dielectric constant K, how does the electric field just outside the surface change?
Answer: B
The electric field just outside a conductor in a dielectric medium is E = σ/(Kε₀), so it decreases by the factor of dielectric constant K compared to vacuum.
Q.227Medium
Two fixed point charges Q₁ = +2μC and Q₂ = -2μC are separated by 2 m. A test charge +1μC is moved along the perpendicular bisector. At what distance from the midpoint (on the bisector) is the electric field maximum?
Answer: B
For an electric dipole, the field along the perpendicular bisector is maximum at distance d = a/√2, where 2a is the separation between charges. Here, a = 1 m, so maximum field is at 1/√2 m.
Q.228Medium
A parallel plate capacitor is filled with two dielectrics of thickness d/2 each and dielectric constants K₁ and K₂. What is the equivalent capacitance if the original capacitance (empty) was C₀?
Answer: D
Dielectrics in series combine like capacitors in series. Total capacitance = (ε₀A × 2K₁K₂)/(d(K₁ + K₂)) = C₀ × 2K₁K₂/(K₁ + K₂).
Q.229Easy
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.230Medium
A hollow conducting sphere of radius R carries charge Q. A point charge q is placed at the center. What is the electric field at distance r from center (r > R)?
Answer: B
By Gauss's law, the field outside depends on the total enclosed charge Q + q. The field is E = k(Q + q)/r² for r > R.
Q.231Easy
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.232Easy
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.233Easy
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.234Easy
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).
Q.235Hard
Two point charges Q and -Q are at distance 2d apart. The potential difference between two points on the perpendicular bisector at distances x and 2x from the midpoint is proportional to:
Answer: C
Using potential superposition and the dipole configuration, ΔV = 2kQd(1/x - 21x) for points on the perpendicular bisector.
Q.236Easy
A conductor of arbitrary shape carries charge Q. Which is constant throughout the conductor?
Answer: B
Inside and on the surface of a conductor in electrostatic equilibrium, the potential is constant everywhere.
Q.237Medium
The electric field just outside a conductor surface is perpendicular to the surface. This is because:
Answer: B
If there were a tangential component of electric field at the surface, charges would move tangentially, violating electrostatic equilibrium. Thus, only the normal component exists.
Q.238Easy
A parallel plate capacitor has plate area A, separation d, and dielectric constant K. Its capacitance is:
Answer: B
The capacitance of a parallel plate capacitor with dielectric is C = Kε₀A/d, where K is the dielectric constant.
Q.239Medium
Three capacitors of capacitance C each are connected in a combination where two are in parallel and this combination is in series with the third. The equivalent capacitance is:
Answer: B
Two capacitors C in parallel: C_parallel = 2C. This in series with C: C_eq = (2C × C)/(2C + C) = 2C/3.
Q.240Medium
A point charge is brought from infinity to a point in an electric field. Work done depends on:
Answer: C
Electric force is conservative; work depends only on initial and final positions (potentials), not on the path taken. W = q(V_initial - V_final).
