Question

A hollow cylindrical box of length 1 m and area of cross-section 25 cm² is placed in a three dimensional coordinate system as shown in the figure. The electric field in the region is given by \(\vec E=50\text x\hat i\), where E is in NC^-1 and x is in metres.

Find

(i) Net flux through the cylinder.

(ii) Charge enclosed by the cylinder.

Answer 1

(i) Electric flux through a surface, φ = \(\vec E.\vec S\)

Flux through the left surface, φ_L = -|E||S| = -50\(\text x\).|S|

Flux through the right surface,

(ii) Charge inside the cylinder, by Gauss's Theorem