An infinitely long conducting cylindrical rod with a positivecharge lambda per u

Question

An infinitely long conducting cylindrical rod with a positivecharge lambda per unit length issurrounded by a conducting cylindrical shell (which is alsoinfinitely long) with a charge per unit length of -2 lambda andradius r1 , as shown in the figure. What is E(r) , the radial component of theelectric field between the rod and cylindrical shell as a functionof the distance r from the axis of the cylindricalrod? Express your answer interms of lambda , r , and epsilon0 , the permittivity offree space.

Explanation / Answer

We know that electric field depends onlyon the distance from the axis of the cylindrical rod. So thatdue symmetry the radial component of the electric field cannot varybetween the rod and cylindrical shell as a function of thedistance r from the axis of the cylindricalrod. Applying gauss law weget                = qinner /o     ............1 We know that the flux through theentire Gaussian surface is                = EA = E(2rl) ........2 From 21 and 2 we get             E(2rl) = qinner /o                 E = qinner / 2rlo                    = /2ro Where qinner =l Where qinner =l

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