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A long cylinder contains charge uniformly distributed throughout its volume with charge density rho C/m³. Find the magnitude of the electric field at a point inside the cylinder located at distance x = 2*epsilon0/rho metres from the axis (answer in V/m).

1. 1 V/m
2. 2 V/m
3. 0.5 V/m
4. 4 V/m

Correct answer: 1 V/m

Solution

For a uniformly charged infinite cylinder, the field inside at radius x is E = rho*x/(2*epsilon0). Substituting x = 2*epsilon0/rho gives E = rho*(2*epsilon0/rho)/(2*epsilon0) = (2*epsilon0)/(2*epsilon0) = 1 V/m.

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