First slide

Electric Flux

Question

A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by:

Moderate

A

$2 {πR}^{2} E$
B

${πR}^{2} / E$
C

$({πR}^{2} - πR) / E$
D

Zero

Solution

Flux through surface $A ϕ_{A} = E \times {πR}^{2} and ϕ_{B} = - E \times {πR}^{2}$
Flux through curved surface
$ϕ_{c} = \int \vec{E} \cdot \vec{d} s = \int Edscos 90^{\circ} = 0$
Total flux through cylinder $= ϕ_{A} + ϕ_{B} + ϕ_{C} = 0$

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