Question

A circular loop in the plane of the paper lies in a 0.61T magnetic field pointing into the paper.

A) If the loop's diameter changes from 19.6cm to 7.4cm in 0.19s , what is the direction of the induced current? (counterclockwise or clockwise)

B) What is the magnitude of the average induced emf?

C) If the coil resistance is 3.7? , what is the average induced current?

Answer 1

given that :

magnetic field, B = 0.61 T

diameter of the loop 1, d₁ = 19.6 cm

radius of the loop 1, r₁ = 9.8 cm = 0.098 m

diameter of the loop 2, d₂ =7.4 cm

radius of the loop 2, r₂ = 3.7 cm = 0.037 m

time taken, dt = 0.19 sec

(A) direction of the induced current is counterclockwise.

(b) magnitude of the average induced emf is given as :

= d / dt                             { eq. 1 }

where, = B . A

inserting the value of '' in above eq.

= B . dA / dt

where, A = area of the circular loop = r²

= B (r₁² - r₂²) / dt                            { eq. 2 }

inserting the values in eq.2

= (0.61 T) (3.14) [(0.098 m)² - (0.037 m)² / (0.19 sec)

= (1.9154) (0.0082) / (0.19) V

= 0.082 V

(c) the average induced current is given as :

using an ohm's law, V = I R                           { eq. 3 }

or I = V / R         

where, V = = average induced emf

resistance, R = 3.7

inserting the values in above eq.

I = (0.082 V) / (3.7 )

I = 0.022 A