Question

A 40-turn coil has a diameter of 11 cm. The coil is placed in a spatially uniform magnetic field of magnitude 0.40 T so that the face of the coil and the magnetic field are perpendicular. Find the magnitude of the emf induced in the coil (in V) if the magnetic field is reduced to zero uniformly in the following times.

(a)

0.30 s

V

(b)

3.0 s

V

(c)

65 s

V

Answer 1

Solution: Total number of turns in the coil, N = 40.

Diameter of coil = 11 cm = 0.11 m

Radius of coil, r = 0.055 m

Initial magnitude of magnetic field, B = 0.40 T

Area of the coil, A =

As the face of the coil and magnetic field are perpendicular to each other. Therefore, angle between the perpendicular to the face of the coil and magnetic field is .

Magnitude of induced emf in the loop is given by,

where,   = induced emf

   = Change in magnetic flux caused by the magnetic field

= Time interval

Initial situation for cases (a), (b) and (c),

So,

And finally, B = 0, therefore

(a)

   

Magnitude of induced emf in the coil if the magnetic field is reduced to zero in time interval 0.30 s, .

(b)

Magnitude of induced emf in the coil if the magnetic field is reduced to zero in time interval 3.0 s, .

(c)  

Magnitude of induced emf in the coil if the magnetic field is reduced to zero in time interval 65 s, .