An electric dipole of moment p is placed in a uniform electric field E at angle θ to the field. The potential energy is:
Answer: A
Potential energy of dipole in electric field: U = -p·E = -pE cos θ. Minimum at θ = 0 (aligned).
Q.245Medium
A non-conducting sphere of radius R is uniformly charged with charge density ρ. What is the electric field at distance r from center (r < R)?
Answer: A
Using Gauss's law with spherical symmetry: E(4πr²) = (ρ × 4πr³/3)/ε₀, giving E = ρr/(3ε₀).
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Q.246Medium
The work done to move a charge q from point A (potential V_A) to point B (potential V_B) is:
Answer: B
Work done by external agent = q(V_B - V_A). If V_B > V_A, positive work is needed.
Q.247Medium
A parallel plate capacitor is filled partially with dielectric (dielectric constant K, thickness d/2) and partially with air (thickness d/2). Its capacitance is:
Answer: B
Capacitors in series: 1/C_total = d/(2ε₀AK) + d/(2ε₀A). Solving: C = 2ε₀AK/[d(K+1)].
Q.248Medium
An electron enters a uniform electric field of strength E with initial velocity perpendicular to the field. Its trajectory is:
Answer: B
Motion is analogous to projectile motion: uniform motion perpendicular to field, accelerated motion along field direction → parabola.
Q.249Medium
A conducting plane carries uniform surface charge density σ. The electric field just outside the surface is:
Answer: B
Using Gauss's law for an infinite charged plane: E = σ/ε₀ (one side only, applies just outside conductor).
Q.250Easy
Two capacitors C₁ and C₂ are connected in parallel across voltage V. The ratio of charges stored is:
Answer: A
In parallel: same voltage V. Q₁ = C₁V, Q₂ = C₂V. Therefore Q₁/Q₂ = C₁/C₂.
Q.251Hard
An insulating rod of length L is uniformly charged with total charge Q. The electric potential at a point on the axis at distance x from one end is:
Answer: A
Integrating potential contributions from small elements: V = (kQ/L)ln[(x+L)/x].
Q.252Medium
A point charge Q is placed at the center of a cubic Gaussian surface of side a. The electric flux through one face is:
Answer: A
Total flux = Q/ε₀. By symmetry, distributed equally over 6 faces: flux per face = Q/(6ε₀).
Q.253Medium
An electric dipole (moment p) is placed in a non-uniform electric field. It experiences:
Answer: C
In non-uniform field: τ = p × E (torque), and F = ∇(p·E) (net force). In uniform field, only torque.
Q.254Medium
The electric field at distance r from an infinitely long uniformly charged line with linear charge density λ is:
Answer: A
Using Gauss's law with cylindrical symmetry: E(2πrL) = λL/ε₀, giving E = λ/(2πε₀r).
Q.255Easy
What is the SI unit of electric dipole moment?
Answer: B
Electric dipole moment p = q × d, where q is charge in Coulombs and d is distance in meters. Unit = C·m
Q.256Medium
A capacitor is charged to potential V and then isolated. If the separation between plates is doubled, what happens to the potential difference?
Answer: A
Since charge Q is constant (isolated capacitor) and C = ε₀A/d, when d doubles, C becomes half. V = Q/C doubles.
Q.257Easy
Two identical metal spheres with charges +Q and -Q are brought in contact and then separated. What is the final charge on each sphere?
Answer: B
When identical conducting spheres touch, charge distributes equally. Total charge = Q - Q = 0. Each sphere gets 0 charge.
Q.258Easy
A point charge q creates an electric potential of 100 V at distance 2 m. What is the potential at distance 8 m from the same charge?
Answer: A
V ∝ 1/r. When distance increases 4 times (2 m to 8 m), potential decreases 4 times: 4100 = 25 V
Q.259Easy
What is the relationship between electric field E and potential V?
Answer: B
Electric field is negative gradient of potential: E = -∇V or E = -dV/dr in one dimension
Q.260Easy
A Gaussian surface encloses charges 2q, -q, and 3q. What is the total electric flux through the surface?
