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

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 = - [tex]\frac{d\phi}{dt}[/tex] = B A sinθ [tex]\frac{d\theta}{dt}[/tex]

Now in the given problem

5 = 0.38 x A x [tex]\frac{d\theta}{dt}[/tex] 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 [tex]\frac{d\theta}{dt}[/tex] Ii

dividing II by I , we have

[tex]\frac{\xi}{5}[/tex] = [tex]\frac{0.55}{0.38}[/tex] = 1.45

or ξ = 7.2 V