Question

A magnetic field is uniform over a flat, horizontal circular region with a radius of 1.90 mm, and the field varies with time. Initially the field is zero and then changes to 1.50 T, pointing upward when viewed from above, perpendicular to the circular plane, in a time of 105 ms.
(a) what is the average induced emf around the border of the circular region?

Answer 1

Answer: 1.61*10^-4 V

Explanation:

Given

Radius of the circular region, r = 1.9 mm = 0.0019 m

time, t = 105 ms

emf = dΦ / dt

ΔΦ = BA where,

ΔΦ is change in magnetic flux

ΔB is the change in the strength of magnetic field

A is the area of the circular region

Area, A = πr² = 3.142 * 0.0019 * 0.0019 = 1.13*10^-5 m²

emf = dΦ / dt

emf = BA / t

emf = (1.5 * 1.13*10^-5) / 105

emf = 1.695*10^-5 / 105*10^-3

emf = 1.61*10^-4 V

Therefore, the average induced emf is 1.61*10^-4 V

Answer 2

Answer:

0.000162V

Explanation:

r = Radius = 1.9 mm

r = 1.9÷1000

r = 0.0019m

emf = dΦ / dt

B_i = Initial magnetic field = 0

B_f = Final magnetic field = 1.5 T

t = Time taken = 105 ms

Induced emf is given by

emf = dΦ / dt

Emf= A ( Bf - Bi )/dt

emf = 3.142 × 0.0019 ×0.0019 × 1.5/ 0.105

end = 0.00001701 ÷ 0.105

emf = 0.0001620 V

Hence the induced elf is 0.0001620V