# Current in a conducting loop

1. Nov 2, 2013

### RenD94

1. The problem statement, all variables and given/known data

A conducting loop with area 0.13m2 and resistance 6.0Ω lies in the x-y plane. A spatially uniform magnetic field points in the z direction. The field varies with time according to Bz=at2−b, where a = 2.8T/s2 and b = 8.0T .

(a) Find the (magnitude of the) loop current when t = 1.3s.

2. Relevant equations

V = I * R
EMF = Δ(BA)/Δt * n

3. The attempt at a solution

I calculated the EMF using the second formula listed, with n = 1 as there is only a single loop.

EMF = Δ(BA)/Δt
Binitial = 2.8(02) - 8 = -8
Bfinal = 2.8(1.32) - 8 = -3.268
=> ΔB = 4.732
=> Δ(BA) = 4.732 * 0.13 = 0.6152

=> EMF = 0.6152 / 1.3 = 0.4732 V

Then I used the first formula to find a value for I...

0.4372 = I * 6
0.0789 A = I

This is incorrect however, and the correct answer given is 0.16 - roughly twice my solution. Am I leaving out a multiplier somewhere? Any help is appreciated, this seemingly simple problem has frustrated me for too long.

2. Nov 2, 2013

### Staff: Mentor

The magnetic field is not changing linearly, so a linear approximation of the change is not going to be too accurate.

Since you have the expression for B(t), I'd suggest using the derivative to find the change in flux since (Faraday's Law):
$$EMF = \frac{d \Phi}{dt}~~~~~~\text{and}~~~~~~\Phi(t) = Area\;B(t)$$

3. Nov 2, 2013

### RenD94

Got it, thanks gneill!
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