Question

In a certain time period a coil of wire is rotated from one orientation to another with respect to a uniform 0.38-T magnetic field. The emf induced in the coil is 5.0 V. Other things being equal, what would the induced emf be if the field had a magnitude of 0.55 T

Answer 1

The emf produced is 7.2 V

Explanation:

When coil is placed in the magnetic field , the flux attached with it can be found by the relation . Flux Ф = the dot product of magnetic field and area of coil .

Thus Ф = B A cosθ

here B is magnetic field strength and A is the area of coil .

The angle θ is the angle between coil and field direction .

When coil rotates , the angle varies . By which the flux varies . The emf is produced in coil due to variation of flux . The relation for this is

The emf produced ξ = - $\frac{d\phi}{dt}$ =  B A sinθ $\frac{d\theta}{dt}$

Now in the given problem

5 = 0.38 x A x $\frac{d\theta}{dt}$                            I

Now if the magnetic field is 0.55 T and all the other terms are same , the emf produced

ξ = 0.55 x A x $\frac{d\theta}{dt}$                              Ii

dividing II by I , we have

$\frac{\xi}{5}$ = $\frac{0.55}{0.38}$ = 1.45

or ξ = 7.2 V