First slide

Electric flux

Question

Flux passing through the shaded surface of a sphere when a point charge q is placed at the center is (radius of the sphere is R)

Difficult

A

$q / ε_{0}$
B

$q / 2 ε_{0}$
C

$q / 4 ε_{0}$
D

$z e r o$

Solution

$\begin{array}{l} α = 60^{\circ} . Solid angle subtended by B C D is \\ ω = 2 π (1 - \cos α) = π \end{array}$
Solid angle subtended by
ABDE is
$\begin{array}{l} ω_{(A B C D E)} - ω_{(B C D)} \\ = 2 π - π = π \end{array}$
Hence, flux through ABDE is
$ϕ = \frac{q}{ε_{0}} \frac{π}{4 π} = \frac{q}{4 ε_{0}}$

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