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A parallel plate capacitor with circular plates of radius R is being charged by a constant current I. Which of the following statements about the fields and energy are correct? (A) The Poynting vector points radially inward everywhere on a cylindrical surface at the rim of the plates. (B) The magnetic field between the plates is clockwise when viewed from above (current flowing upward). (C) The magnetic energy density between the plates is increasing with time. (D) The net Poynting vector flux into the capacitor equals the rate of change of stored energy.

1. (A) Poynting vector points radially inward everywhere on the circle.
2. (B) Magnetic field is clockwise as seen from above.
3. (C) Magnetic energy density is increasing with time.
4. (D) Poynting vector flux is equal to the rate of change of stored energy.

Correct answer: (D) Poynting vector flux is equal to the rate of change of stored energy.

Solution

The magnetic field due to displacement current (counterclockwise from above for upward current) combined with upward E gives S = E x B pointing radially inward. Poynting theorem guarantees flux of S = rate of energy storage. B is false (field is counterclockwise, not clockwise).

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