First slide

Finding field strength using Gauss's Law

Question

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

Difficult

A

$q / ε_{0}$
B

$q / 2 ε_{0}$
C

$q / 4 ε_{0}$
D

Zero

Solution

α =6O°
Solid angle subtended by BCD,
$Ω = 2 π (1 - cosα) = π$
Solid angle subtended by ABDE,
$Ω_{(ABCDE)} - Ω_{(BCD)} = 2 π - π = π$
Hence, flux through ABDE: $ϕ = \frac{q}{ε_{0}} \frac{π}{4 π} = \frac{q}{4 ε_{0}}$

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