Question

A 24-cm circumference loop of wire has a resistance of 0.14 Ω. The loop is placed between the poles of an electromagnet, and a field of 0.55 T is switched on in a time of 15 ms. What is the induced current in the loop?

Answer 1

The induced current in the loop is 1.2 A

Step-by-step explanation:

Given;

length of the wire, L = 24 cm = 0.24 m

resistance of the wire, R = 0.14 Ω.

magnetic field strength, B = 0.55 T

time, t = 15 ms = 15 x 10⁻³ s

Circumference of a circle is given as;

L = 2πr

0.24 = 2πr

r = 0.24 / 2π

r = 0.0382 m

Area of a loop is given as;

A = πr²

A = π (0.0382)²

A = 0.004585 m²

Induced emf is given as;

`emf = -(\delta \phi)/(dt)`

Ф = ΔB x A

Ф = ( 0 - 0.55 T) x 0.004585 m²

Ф = -0.002522 T.m²

`emf = - ((-0.002522)/(15*10^(-3)) )\\\\emf = 0.168 \ V`

According to ohm's law;

V = IR

Where;

I is current

The induced current in the loop is calculated as;

I = V / R

I = 0.168 / 0.14

I = 1.2 A

Therefore, the induced current in the loop is 1.2 A