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A circular conductor of radius a (< b) centred at O is formed by two semicircular halves ABC and ADC. Both segments have the same cross-section but resistances 10 ohm (ABC) and 5 ohm (ADC). A circular region of radius b carries a uniform magnetic field B perpendicular to the plane, increasing with time, inducing an EMF epsilon in the full loop. Which of the following are correct? (A) The ratio of electrostatic fields inside ABC to ADC is 3. (B) The ratio of electrostatic fields inside ABC to ADC is 1:2. (C) Charge accumulated at junction A is negative and at C is positive. (D) Potential difference between A and C is half of the total induced EMF.

1. (A) The ratio of electrostatic fields inside ABC to ADC is 3.
2. (B) The ratio of electrostatic fields inside ABC to ADC is 1:2.
3. (C) Charge accumulated at junction A is negative and at C is positive.
4. (D) Potential difference between A and C is half of the total induced EMF.

Correct answer: (C) Charge accumulated at junction A is negative and at C is positive.

Solution

Current I = epsilon/15. Each segment has length pi*a, so E = IR/(pi*a). E_ABC/E_ADC = 10/5 = 2:1 (so option A says 3: wrong; option B says 1:2: wrong). Potential difference V_A - V_C via path ADC (5 ohm, with EMF epsilon/2 distributed): V_A - V_C = I*5 - epsilon/2 = epsilon/3 - epsilon/2 = -epsilon/6 < 0. So V_A < V_C => junction A is at lower potential => negative charge accumulates at A, positive at C. Option C is correct. |V_AC| = epsilon/6 not epsilon/2, so D is wrong.

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