Question

1)Two parallel uniformly charged ring are placed in 4 meter distance. The charge of one of them is 2c and the other one is -3c.

find the zero point position of the Electric field.

2) Two parallel uniformly charged ring are placed in 4 meter distance. The charge of one of them is 2c and the other one is +3c.

find the zero point position of the Electric field

3) A rod with length "l" is lied along x-axis. The charge density of the rod is "a". Calculate the potential of the rod for a the point p on x-axis.

4) A rod with length "l" is lied along x-axis. The charge density of the rod is "a". Calculate the Electric field of the rod for a point p on x-axis.

5) Using the Gausses law find the electric field of a uniformly charged non conducting cylinder with length L and total charge Q:

a)Inside of it

b)out side of it

Answer 1

For question (1) and (2), diameter of the ring is required to get answer. For both questions, diameter of the ring is not given.

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Qn.(3)

Let us consider left edge coincide with origin for distance measurement.

Let us consider small element of length ds at a distance s from left edge of rod.

Potential dV at point p due to this element of length ds is given by

where a is charge density and ads is the charge on the element ds

Potential V due to full length of rod is given by

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(4)

Elecric field intensity dE at point p due to the element of length ds is given by

Electric field E due to full length of rod is given by

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(4)

Inside charged cylinder , let us consider gaussian surface made of cylinder of radius r and length l

Then by Gauss law, E ( 2r l ) = ( r2 l ) .....................(1)

where E is electric field indtensity at a radial distance r and is volume charge density

From above eqn.(1), we get E = (1/2) r

To get electric field intensity outside of charged cyinder, let us consider gaussian surface that has radius r that is greater than radius R of charged cylinder

Then by Gauss law, E ( 2r l ) = ( R2 l ) .....................(2)

we get, E = (1/2) ( R2 ) ( 1/ r )