Question

The diagram shows a very long, thin line that carries a charge per unit length $\lambda$. A Gaussian cylinder is imagined with its axis along the line and having radius a. The length of the Gaussian cylinder is $L$.
How much charge is enclosed in this cylinder?

• A. $Q_{enc}=2\pi \lambda aL$
• B. $Q_{enc}=\pi \lambda aL$
• C. $Q_{enc}=\lambda L$
• D. $Q_{enc}=\pi \lambda a^{2}L$
• E. $Q_{enc}=2\pi \lambda a^{2}L$

Answer 1

The correct option is C $Q_{enc}=\lambda L$

Length of the Gaussian cylinder $=L$

Charge per unit length $=\lambda$

Thus net charge enclosed in the cylinder $Q_{enc}=\lambda L$