A charge of − 0.560 µC exerts an upward force of magnitude 0.240 N on an unknown charge which is a distance of 0.350 m directly below it.
Part A What is the unknown charge (magnitude and sign)?
Assume that the capacitor has plate area and an electric field between the plates.
Take to be the permeability of free space and to be the permittivity of free space.
The cone-shaped surface shown in the figure has a current passing through it, so Ampère's law indicates a finite value for the field integral around this loop.
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However, a slightly different surface bordered by the same loop passes through the center of the capacitor, where there is no current due to moving charge.
Part A First find , the line integral of around a loop of radius located just outside the left capacitor plate.
This can be found from the usual current due to moving charge in Ampère's law, that is, without the displacement current.
The first term on the right-hand side, , describes the effects of the usual electric current due to moving charge.
In this problem, that current is designated as usual.