Question

Two small charged spheres $A$ and $B$ have charges $10\mu C$ and $40\mu C$ , respectively and are held at a separation of $90cm$ from each other At what distance from $A$, electric intensity would be zero?

• A. 22.5 cm
• B. 18 cm
• C. 36 cm
• D. 30 cm

Answer 1

Answer: (D)

Let a test charge $q_0$ is placed at a point $D$ at a distance $x$ from point $A$.
From Coulombs law, the force on the test charge $q_0$ due to a charge $q$, kept a distance $r$ apart is
$F=-\frac{1}{4\pi {\epsilon }_0}\frac{q{q}_0}{r^2}$
$\therefore$ Electric field intensity at the point $D$ $E=\frac{F}{4\pi {\epsilon }_0}=\frac{1}{4\pi {\epsilon }_0}\frac{q{q}_0}{r^2}$
Let intensity at $D$ distance $x$ from point A be zero,
then $\frac{1}{4\pi {\epsilon }_0}\cdot \frac{10\times 10^{-6}}{x^2}$
$=\frac{1}{4\pi {\epsilon }_0}\frac{40\times 10^{-6}}{(90-x{)}^2}$ $\Rightarrow \frac{1}{x^2}=\frac{4}{(90-x{)}^2}$
$\Rightarrow \frac{1}{x}=\frac{2}{90-x}$
$\Rightarrow$ $90-x=2x$
$\Rightarrow 3x=90$
$\Rightarrow x=30cm$.
Note: The force $F$ acts along the line joining the two charges.