Determine the magnetic field within the capacitor

Reference no: EM13983624

Consider a capacitor with circular parallel plates that have radius r and are separated by a distance d. The capacitor is being charged linearly in time with a constant current I so that q(t) = It.

(a) Determine the electric field within the capacitor as a function of time

(b) Determine the magnetic field within the capacitor as a function of time based on Ampere's law in the following form: ∫B^→.ds^→ = μ₀ε₀dΦE/dt which holds where there is no actual charge current as between the capacitor plates. (Hint: The magnetic field lines are circular within the capacitor)

(c) Determine the Poynting vector S^→ = 1/μ₀ E^→ x B^→ on the surface of the cylindrical volume between the capacitor plates (curved part and on the bases of the cylinder). Make a sketch to illustrate the pattern formed by S^→.

(d) Determine the rate at which energy is flowing into the capacitor by calculating ∫S^→.dA^→ over the surface of the cylindrical volume between the capacitor plates (hint: Notice and describe how the integral simply turns into a product of the value |S| on the curved surface time the area of that surface.)

(e) compare the result of problem (d) to the rate at which the energy stored in the capacitor is increasing.

Reference no: EM13983624

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