A circular loop of wire is immersed in a uniform magnetic field of magnitude 1.0

Question

A circular loop of wire is immersed in a uniform magnetic field of magnitude 1.0muT . The loop is rotating with a constant angular velocity of 1.0times103 rotations per second. The axis of rotation lies in a plane which is perpendicular to the magnetic field. The resistance of the loop is 1.0kohm . The loop encloses an area of 1.0m2.The wire is initially perpendicular to the direction of the magnetic field. Find the magnitude and direction of the induced current in the wire 2.3ms after the loop starts rotating.

Explanation / Answer

Magnetic field strength (B) = 1.0T                                         = 1.0*10-6T Angular frequency () of the loop = 1000 rotations/s Area (A) of the loop = 1.0m2Number of rotations madeby the loop in 2.3 ms is =(1000)(2.3*10-3)rotations/s                                                                                 = 2.3 rotations/s Then emf induced in the loop is = NBA                                                  = (1)(1.0*10-6T)(1.0m2)(2.3 rotations/s)                                                  = 2.3*10-6V Then emf current in the loop is                    I = / R                      = ( 2.3*10-6V) / (1.0*103)                      = 2.3*10-9A                      = 2.3 nA

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