(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An infinite straight wire carries a current I that varies with time as shown above. It increases from 0 at t = 0 to a maximum value I1 = 2.1 A at t = t1 = 14 s, remains constant at this value until t = t2 when it decreases linearly to a value I4 = -2.1 A at t = t4 = 24 s, passing through zero at t = t3 = 21.5 s. A conducting loop with sides W = 20 cm and L = 57 cm is fixed in the x-y plane at a distance d = 49 cm from the wire as shown.

What is ε1, the induced emf in the loop at time t = 7 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise.

2. Relevant equations

B = μI/2∏r

Flux = B*A

-dflux/dt = ε

3. The attempt at a solution

I don't understand what I'm doing wrong with this problem.

This is what I have so far...

(dB*A)/dt= ε, A = L(W)

μ(dI)(L)W/(2∏rdt) = ε

μ=12.566*10^-7

dI = 2.1 A

L = .57 m

W = .2 m

dt=14 s.

On the left side of the box, r = .49 m and the current is negative, so the emf is positive.

On the right side of the box, r = 1.06 m and the current is positive, so the emf is negative.

Putting the 2 emf's together by subtracting the right side from the left side, I get an emf of -3.753*10^-9V.

What am I doing wrong?

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# Homework Help: Time Dependent Current in a wire

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