A long line of charge with charge per unit length runs along the cylindrical axis of a cylindrical conducting shell which carries a charge per unit length of $\lambda$ _c.The charge per unit length on the inner and outer surfaces of the shell, respectively are: A)and $\lambda$_c B)- and $\lambda$_c + - C)- and $\lambda$_c - D) + $\lambda$_c and $\lambda$_c - E) - $\lambda$_c and $\lambda$_c +

Question

Quizplus · Accepted Answer

By Gauss's Law, the electric field outside the cylindrical shell is only due to the linear charge density of the long line of charge along the axis, which is λ_ℓ. Therefore, the field outside the cylindrical shell is given by: E = λ_ℓ / (2πεr) where r is the distance from the axis. Equating this to the electric field due to the charge per unit length F1F1F1S1F1F1F10_c on the cylindrical shell, we get: F1F1F1S1F1F1F10_c = λ_ℓ / (2πεb) where b is the radius of the cylindrical shell. Solving for λ_ℓ, we get: λ_ℓ = (2πεb) F1F1F1S1F1F1F10_c The electric field inside the cylindrical shell is zero, so by Gauss's Law the charge enclosed within the shell must be zero. This means that the charge per unit length on the inner surface must be equal and opposite to that on the outer surface, so that the net charge enclosed is zero. Therefore, the charge per unit length on the inner surface is -λ_ℓ, and the charge per unit length on the outer surface is F1F1F1S1F1F1F10_c + λ_ℓ (since the outer surface has charge per unit length F1F1F1S1F1F1F10_c due to the shell and an additional charge per unit length λ_ℓ due to the long line of charge on the axis). Therefore, the correct choice is B.

A Long Line of Charge with Charge Per Unit λ\lambdaλ

A Long Line of Charge with Charge Per Unit $\lambda$