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). (a) 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. (b) Now consider a location halfway between the capacitor plates, but inside the capacitor at at a radius of r < a. How are the electric and magnetic field strengths changing at this point (i.e. increasing, decreasing, or constant)? Explain your answer. (c) How does the strength of the magnetic field at the location in part (b) compare to the strength of the magnetic field the same radius r from the wire, but away from the capacitor? Explain your answer.

Explanation / Answer

a)   The magnetic field strength at this point is smaller, than the magnetic field the same distance r from the wire .

b)    Electric field strength is constant at this point .

       magnetic field strength is increasing at this point .

c)    the strength of the magnetic field at the location in part (b) compare to the strength of the magnetic field the same radius r from the wire, but away from the capacitor

=> B/B'   =   (pi * r2)/(pi * a2)

               =    (r2)/(a2)

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