First slide

Gauss's Law

Question

One-fourth of a sphere of radius R is removed as shown in figure. An electric field E exists parallel to the xy plane. Find the flux through the remaining curved part

Moderate

A

$π R^{2} E$
B

$\sqrt{2} π R^{2} E$
C

$π R^{2} E / \sqrt{2}$
D

$π R^{2} E^{3}$

Solution

$ϕ_{p l a i n} + ϕ_{c u r v e} = 0$
${\vec{A}}_{1} = - \frac{π R^{2}}{2} \hat{i}, {\vec{A}}_{2} = - \frac{π R^{2}}{2} \hat{j}$
$\begin{array}{l} \vec{E} = E \cos 45^{0} \hat{i} + E \sin 45^{0} \hat{j} \\ ϕ = \vec{E} . ({\vec{A}}_{1} + {\vec{A}}_{2}) \end{array}$

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