Question

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

• A. $\frac{Q}{\varepsilon_{0}}$
• B. $\frac{100 Q}{\varepsilon_{0}}$
• C. $\frac{10 Q}{\pi \varepsilon_{0}}$
• D. $\frac{100 Q}{\pi \varepsilon_{0}}$

Answer 1

Answer: (B)

Charge per metre of the wire $=100 \,Q C$
According to Gauss's law,
The total electric flux passing through the cylindrical surface is
$\phi=\frac{q_{\text {enclosed }}}{\varepsilon_{0}}$
$=\frac{100 \,Q}{\varepsilon_{0}}$