Two charges of magnitude $4 μ C$ and $- 9 μ C$ are $0.5 m$ apart. The electric intensity is zero at a distance x m from A and y m from B. x and y are respectively:

0.5 m, 1.0 m

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1.0 m, 1.5 m

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2.0 m, 1.5 m

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1.5 m, 2.0 m

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Solution

The correct option is B $1.0 m, 1.5 m$
Here, $y = x + 0.5$
Electric field at point P due to charge at A $= E_{1} = \frac{k q_{1}}{x^{2}}$
Electric field at point P due to charge at B $= E_{2} = \frac{k q_{2}}{(x + 0.5)^{2}}$
Here, $q_{1} = 4 μ C$
$q_{2} = - 9 μ C$
$E_{1} + E_{2} = 0$
$⟹ \frac{4}{x^{2}} = \frac{9}{(x + 0.5)^{2}}$
$⟹ x = 1$
$⟹ y = 1.5$

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