Three point charges , and are placed on the -axis at distances , and respectively from the origin, as shown. If and , the magnitude of the net force experienced by the charge is _______ N. [2023]

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Solution

Q.
Three point charges $q$ , $- 2 q$ and $2 q$ are placed on the $x$ -axis at distances $x = 0$ , $x = \frac{3}{4} R$ and $x = R$ respectively from the origin, as shown. If $q = 2 \times 10^{- 6} C$ and $R = 2 cm$ , the magnitude of the net force experienced by the charge $- 2 q$ is _______ N. [2023]

Ans.
(5440)

$F_{B A} = \frac{K q (2 q)}{{(\frac{3}{4} R)}^{2}} = \frac{32 K q^{2}}{9 R^{2}}$

$F_{B C} = \frac{K (2 q) (2 q)}{{(\frac{R}{4})}^{2}} = \frac{64 K q^{2}}{R^{2}}$

$F_{B} = F_{B C} - F_{B A} = \frac{544 K q^{2}}{9 R^{2}}$

$= \frac{544 \times 9 \times 10^{9} \times {(2 \times 10^{- 6})}^{2}}{9 \times {(2 \times 10^{- 2})}^{2}} = 5440 N$

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