A single-turn loop of wire has a resistance of 6.00 Ω and a cross-sectional area 300 cm2 and is perpendicular to a uniform magnetic field which increases at a constant rate from 0.200 T to 3.60 T in 0.500 seconds. What is the magnitude of the induced current in the loop?

A. 0.34 AB. 34 mAC. 2.04 AD. 36 mAE. 0.36 A

Question

Talia

Physics

28 November, 02:33

A single-turn loop of wire has a resistance of 6.00 Ω and a cross-sectional area 300 cm2 and is perpendicular to a uniform magnetic field which increases at a constant rate from 0.200 T to 3.60 T in 0.500 seconds. What is the magnitude of the induced current in the loop?

A. 0.34 AB. 34 mAC. 2.04 AD. 36 mAE. 0.36 A

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Answers (1)

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Mohammad · Answer 1

Given that,

Resistance of wire

R = 6.00 Ω

Cross sectional area

A = 300cm² = 0.03m²

Initial magnetic field Bi = 0.2T

Final magnetic field Bf = 3.6T

Time taken t = 0.5s

Current?

From ohms law

V=iR

Then, I = V/R

Therefore, we need to find the induced EMF in the coil

ε = - dΦ/dt

Where Φ = BA

Where the Area is constant

ε = - dΦ/dt = - d (BA) / dt

Since A is constant

ε = - A•dB/dt

ε = - A• (∆B) / ∆t

ε = - 0.03 (3.6-0.2) / 0.5

ε = - 0.204 V

Then, the magnitude of the EMF is 0.204 V

So,

I = V/R

I = 0.204/6

I = 0.034 Amps

I = 34 mA

Option B is correct.