Magnetism + Sequence = Maquence

An infinitely long, thin, conducting rod is bent in the form of semi-circular rings, as shown in the figure. Now it is placed in a uniform magnetic field of magnitude B0B_0 oriented perpendicular to the plane of the rings.

The radii of the successive half rings are as follows: R,3R2,5R3,7R4R, 3R^2,5R^3,7R^4 \ldots \infty

Now if we rotate the Rod about the point OO with constant angular velocity ω\omega , find the magnitude of the induced emf developed in the rod.


Assumptions

  • The rod is very thin.
  • The rod is rigid.

Details

  • B0=2.0B _0=2.0 Tesla
  • ω=5\omega =5 rad/sec
  • R=0.5R=0.5 m

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