Question

A loop of radius r = 3.0 cm is placed parallel to the xy-plane in a uniform magnetic fieldB= 0.75 Tˆk. The resistance of the loop is 18 Ω. Starting at t = 0, the magnitude of thefield decreases uniformly to zero in 0.15 seconds. What is the magnitude of the electric currentproduced in the loop during that time?

Answer 1

This question is incomplete, the complete question is;

A loop of radius r = 3.0 cm is placed parallel to the xy-plane in a uniform magnetic field B = 0.75 Tˆk.

The resistance of the loop is 18 Ω. Starting at t = 0, the magnitude of the field decreases uniformly to zero in 0.15 seconds.

What is the magnitude of the electric current produced in the loop during that time?

Answer

a 2.1 mA

b 0.79 mA

c 1.7 mA

d 0.20 mA

e 3.9 mA

Answer: option (b) 0.79 mA is the correct answer

Step-by-step explanation:

Given that;

radius r = 3 cm = 0.03 m

Magnetic field B = 0.75

Resistance R = 18

time t = 0.15s

Area A = πr² = π(0.03)² = 0.002827 m²

we know that

Induced EMF ∈ = -BA / T

and ∈ is also = IR

so, IR = -BA/t

I = -BA / Rt

we substitute our values into the equation

I = [- (-0.75 × 0.002827)] / [18 × 0.15]

= 0.002120 / 2.7

= 0.0007851 A ≈ 0.00079 A ≈ 0.79 mA ( milliamperes )

Therefore option (b) 0.79 mA is the correct answer