Question

A closely wound rectangular coil of 80 turns has dimensions of 25 cm by 40 cm. The plane of the coil is rotated from a position where it makes an angle of 37 degrees with a magnetic field of 1.10 T to a position perpendicular to the field. The rotation takes .06 s. What is the average emf induced in the coil?

Answer 1

Answer:

Average emf of coil is 58.4 V

Explanation:

Given :

No. of turns $N = 80$

Area of rectangular coil $A = 0.25 \times 0.40 = 0.1$ $m^{2}$

Magnetic field $B = 1.10$ T

Time of rotation $\Delta t = 0.06$ sec

From the faraday's law,

Average induced emf = $N\frac{\Delta \phi}{\Delta t}$

But flux through coil is given by,

 $\phi = B A \cos \theta$

So we write above equation,

Average induced emf = $\frac{NBA( \cos \theta _{f} - \cos \theta _{i} ) }{\Delta t}$

Where $\theta _{f} = 0$ and $\theta _{i} = 53$   ( $\theta = 37$  angle between plane and magnetic field)

Average induced emf = $\frac{80 \times (1-0.602) \times 1.10 \times 0.1 }{0.06}$

Average induced emf = $58.4$ V