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A long straight cylindrical region has a uniform magnetic field directed along its axis, increasing at a constant rate C (in T/s). A conducting metal wire is placed as an arc of angle pi/3 along a circle of radius R coaxial with the cylinder (R equals the cylinder radius). A voltmeter is connected between the two ends of the wire along a path outside the cylinder. Which of the following statements is NOT correct?

1. Induced emf along the metal wire is = C*pi*R² / 6
2. Induced electric field is non-zero outside the cylinder.
3. Deflection shown by the voltmeter is zero.
4. Deflection shown by the voltmeter is non-zero.

Correct answer: Deflection shown by the voltmeter is zero.

Solution

The induced electric field is non-zero both inside and outside the cylinder (by Faraday's law applied to any enclosing loop). The arc EMF = C*pi*R²/6 is correct. The voltmeter loop encloses flux that changes with time, so it registers a non-zero reading — hence the statement that the voltmeter reads zero is NOT correct.

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