Q. Two small charged spheres $A$ and $B$ have charges $10 \, \mu C$ and $40 \, \mu C$ respectively and are held at separation of $90\, cm$ from each other. At what distance from $A$, electric field intensity would be zero?
Solution:
Given situation is shown in the figure. Suppose electric field intensity at point C is zero.
Here, $AB = r =90\, cm = 0.9\, m$
$q_A = 10\, μC = 10 \times 10^{-6} C$
$q_B = 40\, μC = 40 \times 10^{-6}\, C, AC = ?$
At point $C, E_A = E_B$
$\frac{q_{A}}{4\pi \varepsilon_0 (AC)^2} = \frac{q_{B}}{4\pi \varepsilon_0 (BC)^2} $
$ \frac{q_{A}}{(AC)^2} = \frac{q_{B}}{(r - AC)^2} $
$\frac{10 \times 10^{-6}}{ (AC)^2} = \frac{40 \times 10^{-6}}{ (0.9 - AC)^2} $
$\frac{1}{ (AC)^2} = \frac{4}{ (0.9 - AC)^2} ; \frac{1}{AC} = \frac{2}{ (0.9 - AC)} $
$0.9 -.AC= 2 AC; 3 AC= 0.9$
$AC =0.3 \, m = 30\, cm$
