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.

Explanation:

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