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Question

A wooden stick of length 3l is rotated about an end with constant angular velocity ω in a uniform magnetic
field B perpendicular to the plane of motion. If the upper one third of its length is coated with copper, the
potential difference across the whole length of the stick is

  1. 9Bωl22
  2. 4Bωl22
  3. 5Bωl22
  4. Bωl22


Solution

The correct option is C 5Bωl22

When the rod rotates, there will be an induced current in the rod with copper coating.
The given situation can be treated as if a copper rod of length l rotating in the clockwise direction about an axis at a distance of 2l from one of the corner, with same angular speed  ω

Resultant induced emf will be
e=3l2lBωxdx
e=12Bωl2(94) or e=52Bωl2

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