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Q.

Two spheres A and B are charged with the charges of +10 and +20 coulomb respectively and separated by a distance of 80 cm. The electric field at point on the line joining the centres of the two spheres will be zero at a distance from the sphere A :

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a

20 cm

b

33 cm

c

45 cm

d

60 cm

answer is B.

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Detailed Solution

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$E_{net} = \frac{K (10)}{x^{2}} - \frac{K (20)}{{(80 - x)}^{2}} = 0 \Rightarrow {(\frac{80 - x}{x})}^{2} = 2 \Rightarrow \frac{80}{x} - 1 = \sqrt{2} \Rightarrow \frac{80}{x} = \sqrt{2} + 1 \Rightarrow x = \frac{80}{\sqrt{2} + 1} = \frac{80 (\sqrt{2} - 1)}{2 - 1} = 80 (1.414 - 1) = 80 x 0.414 \approx 33 cm$

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