A circular coil (800 turns, radius = 0.063 m) is rotating in a uniform magnetic field. At t = 0 s, the normal to the coil is perpendicular to the magnetic field. At t = 0.016 s, the normal makes an angle of 45o with the field because the coil has made one-eighth of a revolution. An average emf of magnitude 0.042 V is induced in the coil. Find the magnitude of the magnetic field at the location of the coil.

0.000099T

Explanation:

For a circular coil the flux through a single turn changes by :

∆ = BAcos45° - BAcos90°

= BA cos 45°

During the interval of ∆t = 0.0165s

For N turn, Faraday's law gives the magnitude of emf as follows :

/E/= / -N BAcos45°/ ÷ ∆t

Since the loops are circular the area A of each loop is equal to πr square

B = /E/ ∆t ÷ Nπr square cos45°

= 0.042V × 0.0165/ 800 × 3.142 × 0.063^2 cos 45°

= 0.000693/7

= 0.000099T

= 9.9×10^-5T

The answer is 15.