First slide

Gauss's Law

Question

A hemispherical body is placed in a uniform electric field E. What is the flux linked with curved surface, if field is perpendicular to base in figure.

Moderate

A

$2 {πR}^{2} E$
B

${πR}^{2} E / 2$
C

${πR}^{2} E$
D

0

Solution

Let us consider that the given hemispherical body as a closed surface (whose flux is $ϕ$ ₂ ) In this case, the electric flux linked with the body is zero since the body does not enclose any charges:
$ϕ = ϕ_{1} + ϕ_{2} = 0$
$\Rightarrow ϕ_{1} = - ϕ_{2}$ ………………(1)
Since the field acts perpendicular to the base, the flux linked with the base is given by
$ϕ_{2} = E \times {πR}^{2} \cos 180^{\circ} = - {πR}^{2} E$
Therefore, the flux linked with the curved surface is
$\Rightarrow ϕ_{1} = - ϕ_{2} = - (- {πR}^{2} E) = {πR}^{2} E$

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