A circular parallel plate capacitor with radius a = 2.5 cm and plate separation

Question

A circular parallel plate capacitor with radius a = 2.5 cm and plate separation d = 1.0 mm is connected to an infinitely long wire as pictured. A switch is closed at t = 0 s, and the capacitor is charged with a constant current of I(t) = 0.5 A. Assume that the capacitor is ideal (i.e., there is no electric field outside the plates). Consider a location halfway between the capacitor plates, but at a radius of r > a (i.e. outside the capacitor itself.) Is the magnetic field strength at this point larger, smaller, or the same as the magnetic field the same distance r from the wire, but away from the capacitor? Explain your answer. Now consider a location halfway between the capacitor plates, but inside the capacitor at at a radius of r

Explanation / Answer

The capacitor does allow for displacement current which is the same as that of the charging current. So B at r > a is same as the B at distance r from the wire away from the capacitor

E is increasing ( because stored charge is increasing)
B is decreasing (assuming that the capacitor is charging and hence the I is dexreasing)

If we assume I to be constant, then B inside the capacitor would be same as if it were a distance R from the wire away from the capacitor

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