Question

A circular coil (d = 28 cm, N = 113 turns) is placed in a region of space where there is no magnetic field. Suddenly, a magnetic field is turned on and the coil is totally immersed in it. The magnetic field reaches the strength of 950 mT in 3.5 ms.

1. Determine the voltage induced across the coil

2. Determine the current through a 23 Ω resistor connected across the coil.

Answer 1

When the magnetic field is turned on and the coil is totally immersed in it, there is an induced emf (voltage) in the coil. The voltage generated can be calculated by Faraday’s law of electromagnetic induction given as

where, N= Number of turns =113

Diameter of coil,d=28cm

Radius of coil,r=d/2=14cm

Area of coil=πr² = 3.14*(14) ² cm² = 615.44 cm²

Since there is a change in strength of magnetic field from 0T to 950 mT in 3.5 ms

Therefore,

V_ind = -113 *(615.44*10^-4) * ((0-950)/3.5)

= 1887.6424 V

Current through a 23 Ω resistor connected across the coil is given as

i = V_ind / R

= 1887.6424/ 23

=82.07 A