Calculating EMF Around a Square in a Magnetic Field

[gadje]

Homework Statement

A square of side 2cm, in the first quadrant of the x-y plane, with a corner at the origin, is in a magnetic field pointing out of the page of magnitude 4t²y.

Calculate the emf around the square at t = 2.5s and give its direction.

Homework Equations

$$\epsilon = - \frac{d}{dt} \Phi$$

The Attempt at a Solution

Do I do it like this?

$$\epsilon = -\frac{d}{dt} \int ^2 _0 \int ^2 _0 4t^2 y \ dx \ dy$$

If so, then great. If not, what do I do?

 

[alexgmcm]

Yeah, that seems correct as you are just using the definition of flux:
$$\phi = \int \vec{B} \cdot \vec{dA}$$

And subbing that into your above expression for the emf.

It looks correct but I'm not certain as I'm only a mere first year so you should probably get someone else to confirm.

 

[stevenb]

It looks correct, but I would double check the units of distance, magnetic field and voltage. What system of units are you using for Maxwell's equations? I normally use SI units with meters, Telsa and Volts, so I would have set my upper limits at 0.02 rather than 2. However, if you are using CGS units it may be correct - just double check it.

 

[gadje]

Yeah, I screwed up the units in the OP; had them right in my paper calculation.

 

[stevenb]

Yeah, I screwed up the units in the OP; had them right in my paper calculation.

OK, good! I guess you're using SI units. I think with cgs (or, more accurately Gaussian) units there might be a speed of light factor involved.