A 10 A current is charging a 1.0-cm diameter parallel-plate capacitor. (a) What is the magnetic field strength at a point 2.0 mm radially from the center of the wire leading to the capacitor? (b) What is the magnetic field strength at a point 2.0 mm radially from the center of the capacitor?

Please see explanation for the first part.

Explanation:

Part 1. Use Ampere's law and find the B field from a wire. If you set up a drawing, you would have a wire, with current 10 A. You can draw an amperian loop about the wire, with distance r = 0.002 m. Using Ampere's law:

= mu * I (capitalized letter i, current through the amperian).

Mu naught is the permeability constant 4pi*10^-7. The ds component is an arc length which becomes r*dθ. The B field we assume is uniform and constant, so pull B out of the integral. Also since radius r is constant pull it out as well. Once done, then you will integrate dθ, from 0 to 2pi, a full circle. On the left side of the equation you will get B*2*pi*r. On the left, you can plug in the permeability constant and the current given (since the current through the amperian loop incorporates the total current).

Then isolate B, by dividing mu I by 2 pi r, to get your answer. I would recommend converting to SI units, or at least keep the units consistent.  

0.19 m/s and 0.45 m/s

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