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An infinite cylinder of radius R has a linear charge density . The volume charge

ID: 1408034 • Letter: A

Question

An infinite cylinder of radius R has a linear charge density . The volume charge density (C/m3) within the cylinder (rR) is (r)=0rR, where 0 is a constant to be determined.

A.) The charge within a small volume dV is dq=dV. The integral of dV over a cylinder of length L is the total charge Q=L within the cylinder. Use this fact to to determine the constant 0 in terms of and R.

Hint: Let dV be a cylindrical shell of length L, radius r, and thickness dr. What is the volume of such a shell?

Express your answer in terms of the variables , R, and appropriate constants.

B.) Use Gauss's law to find an expression for the electric field E inside the cylinder, rR. Give your answer as a multiple of /0.

Express your answer in terms of the variables r, R, and appropriate constants.

Explanation / Answer

a)use given condition,find out first q value by doing integration.then write vol=area length

differetiate it and substitute in integration part so rho0(constant)=lamda/pi*R*r2