The double integral definitely makes the most sense. Like I stated in the original post, I was curious if it could be solved without the double integral since the course doesn't have multivariable calculus as a pre-req. Seemed strange to have problems with double integrals without a foundation...
Excellent; thank you. I do apologize for the confusion in the beginning.
Just out of curiosity, is it possible to solve the integral without resorting to a double integral? I don't see anyway to, since you have both A and E varying radially outwards (its not like A is constant, simplifying...
The surface is a circle, not a sphere. I found a picture of the region online, sorry for not including it originally. I'm finding the induced magnetic field at a radial distance from the center of this region; the electric field is coming out of the page in that picture, and its magnitude...
So since the integral depends only on two variables, of which time is neither, the time-derivative can essentially be freely taken before or after integration?
Thanks for the detailed proof as well.
Yes, it does come with a diagram, but it's just a drawing of a circle so I didn't think it was...
Homework Statement
An electric field is directed out of the page within a circular region of radius R = 3.00 cm. The field magnitude is E = (0.500 V/ms)(1 - \frac{r}{R})t, where t is in seconds and r is the radial distance (r≤R). What is the magnitude of the induced magnetic field at a...