First slide

Types of charge distribution

Question

A positive charge ‘Q’ is distributed uniformly throughout an insulated sphere of radius R, centered at origin. A positive charge ‘Q’ is placed at x = 2R on the x-axis. The magnitude of the electric filed at $x = \frac{R}{2}$ on the x-axis will be

Difficult

A

$\frac{3 Q}{16 π \in_{0}} R^{2}$
B

$\frac{Q}{32 π \in_{0}} R^{2}$
C

$\frac{5 Q}{72 π \in_{0} R^{2}}$
D

$\frac{Q}{72 π ϵ_{0} R^{2}}$

Solution

$\bar{E} = {\bar{E}}_{1} + {\bar{E}}_{2}$
$E = \frac{Q}{4 π ϵ_{0}} [\frac{x_{1}}{R^{3}} - \frac{1}{x_{2}^{2}}]$
$\begin{array}{l} = \frac{Q}{4 π ϵ_{0}} [\frac{R / 2}{R^{3}} - \frac{1}{(3 R / 2)^{2}}] \\ = \frac{Q}{72 π ϵ_{0} R^{2}} \end{array}$

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