Question

Electric charge is uniformly distributed along a long straight wire of a radius of 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 as shown in fig. The total flux passing through the cylindrical surface is:

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

Answer 1

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

Charge enclosed by cylindrical substance (length $100cm$) is

${\varphi }_{enc}=100\varphi$

By applying Gauss's law

$\varphi =\frac{1\times {\varphi }_{enc}}{{\epsilon }_0}=\frac{100\varphi }{{\epsilon }_0}$