# Gauss Law applied to charged rod and cylinder

1. the electric field just above the surface of the charged drum of photocopying machine has a magnitude E of 2.3X10^5 N/C. What is the surface charge density on the drum, assuming the drum is conductor?

2.A charge of uniform linear density 2.0nC/m is distributed along a long thin nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius=5.0cm, outer radius=10cm) The net charge on the shell is zero.

(a)What is the magnitude of the electric field 15 cm from the axis of the shell?

(b)What is the surface charge density on the inner and outer surface of the shell?

I really appreciated the help, thank you.

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Correction: An error is fixed. Please read the note at the end of this solution.

1. Use Gauss' law. Imagine an area of A on the surface of a drum. Flux out of this area is = E A.

According to Gauss' law, E A = Q/εo where εo is the permittivity of ...

#### Solution Summary

This solution set contains the solution to two questions in electricity and magnetism. These questions are very common and students encounter them very often in physics exams and quizzes. I have provided step by step solution to both of them using Gauss's law.

Four problems on electric field, charge, flux, charge density

1. A conducting rod of radius R1 = 1.57mm and length l=13.9m inside a thin-walled coaxial conducting cylindrical shell of radius R2=13.0R1 and the (same) length l. The net charge on the rod is Q1= +3.43 x 10^-12C; that on the shell is Q2= -2.32Q1. a) What is the magnitude and direction [radially inward or outward] of the electric field at radial distance r=2.00R2? b) What is the magnitude and direction at r=5.01R1? c) What is the charge on the interior and exterior surface of the shell? Give electric fields in N/C and charges in Coulombs.

2. A point particle with charge q=80uC is placed at a corner of a cube of edge a=8.1cm. What is the flux through each cube face forming the corner? and each of the other cube faces?

3. A small, nonconducting ball of mass m=1.3mg and charge q=2.6 x 10-8C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle theta=39 degrees with a vertical, uniformly charged nonconducting sheet. Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surface charge density of the sheet.

4. An electron enters a region of uniform electric field with an initial velocity of 48 km/s in the same direction as the electric field, which has magnitude E= 71 N/C. What is the speed in (km/s) of the electron 3.0 ns after entering this region? How far (in microns) does the electron travel during the 3.0 ns interval?

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