A 119 turn119 turn circular coil of radius 2.47 cm2.47 cm is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. Over an interval of 0.167 s0.167 s, the magnetic field strength increases from 57.9 mT57.9 mT to 96.9 mT96.9 mT. Find the magnitude of the average emf  avgEavg induced in the coil during this time interval, in millivolts.

Given that,

Number of turns is 119

N = 119

The radius of the coils is 2.47 cm

R = 2.47 cm = 0.0247m

Then, the area of the circular coil is given as

A = πr²

A = π * 0.0247²

A = 1.917 * 10^-3 m²

Time interval

t = 0.167s

The magnetic field strength increases from B1 = 57.9mT to B2 = 96.9 mT

Then,

∆B = B2 - B1 = 96.9 - 57.9 = 39 mT

∆B = 39 * 10^-3 T

We want find the average emf

EMF induced in a coil is given as

ε = - N dΦ / dt

Then, magnetic flux (Φ) is given as

Φ = BA

Then,

ε = - N dΦ / dt

ε = - N d (BA) / dt

Since the area is constant, so we have

ε = - N•A dB / dt

ε = - N •A • ∆B / ∆t

So, inserting the parameters above

ε = - 199 * 1.917 * 10^-3 * 39 * 10^-3 / 0.167

ε = 0.0891 V

To mV

ε = 89.1 * 10^-3 V

ε = - 89.1 mV

Then, the magnitude of EMF induced in the coil is 89.1 mV