First slide

Electric field

Question

A spherical shell of radius R = 1.5 cm has a charge $q = 20 μ C$ uniformly distributed over it. The force exerted by one half over the other half is

Moderate

A

zero
B

$10^{- 2} N$
C

$500 N$
D

$2000 N$

Solution

$\begin{array}{l} E = \frac{σ}{2 ε_{0}} \\ F = E d q = \frac{σ d A σ}{2 ε_{0}} \\ P = \frac{F}{d A} = \frac{σ^{2}}{2 ε_{0}} \end{array}$
$\begin{matrix} Force = P π R^{2} = \frac{σ^{2}}{2 ε_{0}} π R^{2} = \frac{Q^{2}}{16 π^{2} R^{4}} \frac{π R^{2}}{2 ε_{0}} = \frac{Q^{2}}{32 π ε_{0} R^{2}} \\ = \frac{{(20 \times 10^{- 6})}^{2} \times 9 \times 10^{9}}{8 {(1.5 \times 10^{- 2})}^{2}} = 2000 N \end{matrix}$

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