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?

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

option (b) 0.79 mA is the correct answer

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

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