A long, straight wire is surrounded by a hollow metal cylinder whose axis coinci

Question

A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of lambda, and the cylinder has a net charge per unit length of 2 lambda. From this information, use Gauss's law to find the following. (Use any variable or symbol stated above along with the following as necessary: epsilon_0 and pi.) the charge per unit length on the inner surface of the cylinder lambda_ inner = _______________ the charge per unit length on the outer surface of the cylinder lambda_ outer = ____________ the electric field outside the cylinder a distance r from the axis magnitude E = _____________ direction

Explanation / Answer

a.) The charge per unit length on the inner surface of the cylinder is -

Because in electrostatics, the electric field inside a conductor is zero since the charges reside only on the surface of the conductor. For, that to happen, the net charge inside a cylindrical gaussian surface inside the conductor and coaxial to the cylinder should be zero.

Hence, if the charge per unit length of the inner wire is then the charge per unit length of the inner surface of the cylinder is -

b.) Since the net charge per unit length of the cylinder is given as 2

2 =charge per unit length on the inner surface + charge per unit length on the outer surface

2 = - + charge per unit length on the outer surface

charge per unit length on the outer surface = 2 + = 3

c.) Assume a cylindrical Gaussian surface with radius more than the radius of the cylinder and coaxial with the axis of the cylinder.

By applying Gauss' law,

Flux through the Gaussian surface = net charge / o

E x 2rL = 3 L / o

E = 3/ 2ro   in the radially outward direction assuming to be positive.

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