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An L-shaped conducting frame rotates with constant angular velocity omega = 2 rad/s about the corner O inside a uniform magnetic field B = 1 T directed perpendicular to the plane of rotation. The two arms of the L-frame are OA (length 2 m) and OB (length 4 m). Find V_B - V_A in volts.

1. 8
2. 12
3. 16
4. 24

Correct answer: 12

Solution

For a conducting rod rotating about one end in a uniform field, the potential difference between the end and pivot is (1/2)*B*omega*L². With L_OA = 2 m and L_OB = 4 m, V_B - V_A = (1/2)*1*2*(16 - 4) = 12 V.

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