The figure below shows a circuit containing a resistor and an uncharged capacitor. Pointing into the plane of the circuit is a uniform magnetic field. If the magnetic field reverses direction in a short period of time, which plate of the capacitor (top or bottom) becomes positively charged? Explain.
The changing magnetic field flux induces the electric field and corresponding electromotive force around the magnetic field, which is proportional to the rate of change of magnetic field flux. The direction of the induced electric field is such as to oppose the change in the magnetic field flux that created the induced electric field, according to the Lenz Law.
Answer and Explanation:
The top plate will be charged positively.
The induced emf and the respective current will be such as to oppose the change in the magnetic field flux that created them. Since the magnetic field changed direction from into to out of page, the induced field will be into the page, to oppose the change and try to maintain the same flux. According to the right-screw rule, the direction of circulation of the current is the same as the direction of rotation of the right-hand screw if driven in the direction of the magnetic field. The induced field, as we already established, is into the page, therefore, the direction of rotation of the right-hand screw has to be clockwise in order to be driven into the page. Therefore, the induced current is in the clockwise direction. Since the current is, by agreement, a flow of positively charged particles, the positively charged particles will move in the clockwise direction. Therefore, they will accumulate on the top plate until the voltage is high enough to stop any further flow of the current.
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from GACE Physics (530): Practice & Study GuideChapter 23 / Lesson 9