A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. What is the electric potential at the center of the cylinder ?
The electric potential is
A hollow cylindrical shell with a radius of R and a length of L has a uniform charge distribution along its length, resulting in a total charge of Q.
The electric potential at a distance r from a point charge q is calculated as follows:
Potential along the central axis of a ring of radius R having charge q, at a distance from the center,
Consider a ring with a width of and a distance of x from the cylinder's center. The charge per square meter of cylinder area,
The ring element's charge,
Therefore, the potential at the center of the cylinder due to ring element
As a result of the whole charge distribution, the potential at the cylinder's core,
The potential at the center of the cylinder is found to be
charge and a charge are located on the x-axis at and , respectively.
a. Other than at infinity, is there a position or positions on the x-axis where the electric field is zero? If so, where?
b. Other than at infinity, at what position or positions on the x-axis is the electric potential zero?
c. Sketch graphs of the electric field strength and the electric potential along the x-axis.
A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal sphere. A typical classroom-demonstration model has a diameter of .
a. How much charge is needed on the sphere for its potential to be ?
b. What is the electric field strength just outside the surface of the sphere when it is charged to ?
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