A uniformly charged infinite line with linear charge density λ creates an electric field at perpendicular distance r. What is E?
Answer: B
Using Gauss's law for infinite line: E = λ/(2πε₀r). This is standard result for line charge.
Q.42Hard
Three point charges are arranged at the vertices of an equilateral triangle of side a. If charges are +q, +q, and -2q, what is the net electric potential at the centroid?
Answer: A
Distance from each vertex to centroid is a/√3. V = k(q + q - 2q)/(a/√3) = 0. The charges sum to zero, giving zero potential.
Q.43Hard
A charge Q is uniformly distributed on a ring of radius R. What is the electric potential at a point on the axis at distance x from the center?
Answer: A
All charge elements on the ring are equidistant from the axial point. Distance = √(R² + x²), so V = kQ/√(R² + x²).
Q.44Hard
Consider a uniformly charged disc of radius R with total charge Q. What is the electric field at the center of the disc?
Answer: B
For a uniformly charged disc, the field at the center involves integrating contributions from rings. Result: E = σ/(2ε₀) = Q/(2πε₀R²).
Q.45Hard
Two point charges q₁ = 2 μC and q₂ = -2 μC are separated by 1 cm. What is the magnitude of electric field at the midpoint between them?
Answer: A
At midpoint, distance from each charge = 0.5 cm = 0.005 m. Both fields point in same direction (from +q toward -q). E_total = 2 × k × 2×10⁻⁶ / (0.005)² = 7.2 × 10⁷ V/m.
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Q.46Hard
A spherical conductor of radius R is grounded and placed near an isolated point charge +Q at distance d from its center (d > R). Which statement is correct about the induced charge on the sphere?
Answer: A
The grounded sphere develops negative charge to maintain V = 0. The charge distribution is non-uniform because the near side accumulates more negative charge.
Q.47Hard
The sensitivity of a galvanometer can be increased by:
Answer: D
Sensitivity θ ∝ NAB/k. It increases with more turns (N) and weaker torsional constant (k). Both B and C increase sensitivity.
Q.48Hard
A wire of length L and cross-sectional area A has resistance R. If the wire is stretched to length 2L without change in volume, the new resistance will be:
Answer: B
When stretched, volume constant: A × L = A' × 2L → A' = A/2. New resistance R' = ρ(2L)/(A/2) = 4ρL/A = 4R.
Q.49Hard
The equivalent resistance between two opposite corners of a cube made of 12 wires of 1Ω each is:
Answer: B
Due to symmetry, current divides into three paths of 1Ω each in parallel at the first vertex, then similar distribution at other vertices. Equivalent = 31 + 61 + 31 = 65Ω
Q.50Hard
A heating element of resistance R is connected to a battery of EMF E and internal resistance r. Maximum power is dissipated in R when:
Answer: B
By maximum power transfer theorem, maximum power is transferred to external load when load resistance equals internal resistance
Q.51Hard
Which of the following best explains why semiconductor resistance decreases with increase in temperature?
Answer: C
In semiconductors, increased temperature promotes more electrons from valence to conduction band, increasing carrier concentration and decreasing resistance
Q.52Hard
A battery of EMF 12V and internal resistance 2Ω is connected to a load resistance R. For maximum power transfer, R should be:
Answer: B
Maximum power transfer theorem: Load resistance equals internal resistance. R = r = 2Ω for maximum power
Q.53Hard
The electric field inside a copper conductor carrying current is approximately:
Answer: B
By Ohm's law in microscopic form: E = ρJ. Inside the conductor, electric field maintains the drift of electrons
Q.54Hard
When a superconductor is cooled below its critical temperature, its resistance becomes zero. What is the effect on current flowing through it when connected to a constant voltage source?
Answer: A
With R = 0, by I = V/R, current becomes infinite. In practice, voltage source cannot be maintained across a superconductor
Q.55Hard
The length of a conductor increases by 10% when stretched. Assuming volume remains constant, the resistance increases by approximately:
Answer: C
R = ρL/A. If L increases by 10% and volume constant, A decreases by ~9.1%. New R = 1.1R₀/0.91 ≈ 1.21R₀, so 21% increase.
Q.56Hard
The equivalent resistance of an infinite ladder network of 1Ω resistors (each rung) is:
A superconductor exhibits zero resistance below its critical temperature because:
Answer: B
BCS theory explains superconductivity: below critical temperature, electrons form Cooper pairs with no scattering, resulting in zero resistance.
Q.58Hard
In a Wheatstone bridge, arms P, Q, R, and S have resistances 10Ω, 15Ω, 20Ω, and 30Ω respectively. A galvanometer is connected between junctions of P-Q and R-S. The galvanometer reading will be:
Answer: A
For balanced bridge: P/Q = R/S. Check: 1510 = 3020 → 32 = 32. The bridge is balanced, so no current flows through galvanometer (zero reading).
Q.59Hard
A circular loop and a square loop of equal perimeter are placed in the same uniform magnetic field. Their magnetic moments are:
Answer: B
For equal perimeter, circle encloses maximum area (isoperimetric inequality). Since magnetic moment m = IA, circular loop with larger area has larger magnetic moment.
Q.60Hard
A charged particle moves in crossed electric and magnetic fields. For the particle to move undeflected, the condition is:
Answer: A
For undeflected motion, electric and magnetic forces must balance: qE = qvB, giving E = vB. This is the principle of velocity selector used in mass spectrometers.
