Question

Electric charge is uniformly distributed along a long straight wire of radius $1mm$. The charge per $cm$ length of the wire is $Q$ coulomb. Another cylindrical surface of radius $50cm$ and length $1m$ symmetrically encloses the wire. The total electric flux passing through the cylindrical surface is

• A. $\frac{Q}{{\epsilon }_0}$
• B. $\frac{100Q}{{\epsilon }_0}$
• C. $\frac{10Q}{\pi {\epsilon }_0}$
• D. $\frac{100Q}{\pi {\epsilon }_0}$

Answer 1

Answer: (B)

Charge per metre of the wire $=100QC$
According to Gauss's law,
The total electric flux passing through the cylindrical surface is
$\varphi =\frac{q_{\text{enclosed }}}{{\epsilon }_0}$
$=\frac{100Q}{{\epsilon }_0}$