Question

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

• A. 20 cm
• B. 33 cm
• C. 55 cm
• D. 60 cm

Answer 1

The correct option is B 33 cm

Let, $x$ between $A$ electric field is zero.

$F=\frac{1}{4\pi {ϵ}_0}\frac{q}{r^2}$

$\therefore$ $E$ is zero

or, $\frac{10}{x^2}=\frac{20}{{(80-x)}^2}$

Taking square root

$\frac{\sqrt{10}}{x}=\frac{\sqrt{20}\sqrt{2}}{80-x}$

$80-x=\sqrt{2}x$

or, $80=\sqrt{2}x+x$

or, $80=(\sqrt{2}+1)x$

or, $x=\frac{80}{\sqrt{2}+1}=33cm$