Electric charge is uniformly distributed along a long straight wire of radius \(1 \mathrm{~mm}\). The charge…
Electric charge is uniformly distributed along a long straight wire of radius \(1 \mathrm{~mm}\). The charge per \(\mathrm{cm}\) length of the wire is \(\mathrm{Q}\) coulomb. Another cylindrical surface of radius 50 \(\mathrm{cm}\) and length \(1 \mathrm{~m}\) symmetrically encloses the wire as shown in the figure. The total electric flux passing through the cylindrical surface is \(\mathrm{K} \frac{Q}{\varepsilon_{0}}\), where \(\mathrm{K}\) is a positive integer. Find K.
Solution
Charge enclosed by a cylindrical surface (length \(100 \mathrm{~cm}\) ) is \(\mathrm{Q}_{\mathrm{enc}}=100 \mathrm{Q}\). By applying
\(\text {Gauss's law } \phi=\frac{1}{\varepsilon_{0}}\left(Q_{e n c .}\right)=\frac{1}{\varepsilon_{0}}(100 Q)\)
Asked in: JEE Mains - Electrostatics - Chapter Test
