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 \(B_0\) oriented perpendicular to the plane of the rings.

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

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


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


  • \(B _0=2.0\) Tesla
  • \(\omega =5\) rad/sec
  • \(R=0.5\) m

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