Question

A magnetic field is directed North and is increasing at a rate of 2.0 T/sec. A wire loop with N=10 turns, area 1.0 square centimeter, and resistance R= 1.00 ohms is facing horizontally with its normal vector pointed North. What is the magnitude of the current (in Amps) in the wire loop?

Answer 1

Step-by-step explanation:

Given that,

Rate of increase of magnetic field

dB/dt = 2 T/s

Number of turns N = 10

Area of surface.

A = 1cm² = 1×10^-4 m²

Resistance R =1 ohms

From ohms law

V = iR

So, I = V/R

We need to find the induced EMF in the coil

Then, EMF is given as

ε = -N•dΦ/dt

Where Φ = BA

A is constant

ε = -N•dΦ/dt = -N•d(BA)/dt

ε = -N•A•dB/dt

Then,

ε = - 10 × 1×10^-4 × 2

ε = 0.002 V

Then, applying ohms la

I = V/R

I = 0.002/1

I = 0.002 Amps

I = 2 mA