Q .80 - Excercises And ProblemsExpert-verified
Charge is uniformly distributed with charge density \rho inside Calc a very long cylinder of radius R. Find the potential difference between the surface and the axis of the cylinder.
The potential difference between the surface and axis of the cylinder
Charge is uniformly distributed with charge density \rho inside a very long cylinder of radius R.
If represents electric field and V represents potential associated with it then they are related by
Gauss's law, E.
electric field through the surface of area A
charge enclosed by the suiface
Permittivity of vacuum
Consider a Gaussian surface inside the cylinder with radius r
Applying Gauss's law to the Gaussian surface,
So potential difference between the surface and axis of the cylinder is given by,
Two 5.0 mm * 5.0 mm electrodes are held 0.10 mm apart and are attached to a 9.0 V battery. Without disconnecting the battery, a 0.10-mm-thick sheet of Mylar is inserted between the electrodes. What are the capacitor’s potential difference, electric field, and charge
(a) before and
(b) after the Mylar is inserted?
The two metal spheres in Figure Q26.9 are connected by a metal wire with a switch in the middle. Initially the switch is open. Sphere 1, with the larger radius, is given a positive charge. Sphere 2, with the smaller radius, is neutral. Then the switch is closed. Afterward, sphere 1 has charge , is at potential , and the electric field strength at its surface is . The values for sphere 2 are .
a. Is larger than, smaller than, or equal to ? Explain.
b. Is larger than, smaller than, or equal to ? Explain.
c. Is larger than, smaller than, or equal to ? Explain.
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