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 50 cm and length 1m symmetrically encloses the wire as shown in the figure. The total electric flux passing through the cylindrical surface is

• A. $\frac{Q}{{ϵ}_0}$
• B. $\frac{100Q}{{ϵ}_0}$
• C. $\frac{10Q}{\left(\pi {ϵ}_0\right)}$
• D. $\frac{100Q}{\left(\pi {ϵ}_0\right)}$

Answer 1

The correct option is B $\frac{100Q}{{ϵ}_0}$

Charge enclosed by cylindrical surface (length 100 cm) is $Q_{exc}=100Q.$ By applying Gauss's law
$\varphi =\frac{1}{{ϵ}_0}\left(Q_{e\gamma \alpha }\right)=\frac{1}{{ϵ}_0}\left(100Q\right)$