# Calculate the magnitude of the induced EMF in the loop

1. Apr 7, 2015

### Shinwasha

1. The problem statement, all variables and given/known data
A square conducting loop lies in the xy plane of an xyz coordinate system. The loop is in a uniform magnetic field that points in the positive z direction and is decreasing at a rate of 0.070 T/s. What are (a) the magnitude of the induced EMF in the loop and (b) the direction of the induced current?

2. Relevant equations
Ɛ = ∆Φ / ∆t
∆Φ = A∆B
3. The attempt at a solution

Area = .04m^2
∆Φ = .04m^2 * 0.070 T/s = .028 T*m^2/s

I'm thinking the ∆t is going to be 1 second since no other time interval was given. Therefore Ɛ = ∆Φ / ∆t = .028/1 = .028 T*m^2

As for (b) since the magnetic force is decreasing the current is going to increase in order to conserve the magnetic field. Therefore the induced magnetic field will be in the positive z direction. Therefore the current turns in CCW

2. Apr 7, 2015

### collinsmark

I think you're off by an order of magnitude, in that I think you missed a zero in your calculations somewhere.

More on your treatment of $\Delta \Phi$ below.
There's really no need to make such an assumption. 0.070 T/s is already the rate of change of the field. It has the $\Delta t$ included in it already. -0.070 T/s = $\frac{\Delta B}{ \Delta t}$.

Missing a zero as was mentioned (see above). [Edit: and as discussed above, there is no need to make assumptions about $\Delta t$ being a specific value such as 1 second -- it's already built into the existing units.]

I think you are correct on this part. Although if you mention CW or CCW you may wish to specify whether it's viewed from above or below to avoid ambiguity.

Last edited: Apr 7, 2015