Browse Questions

# Two point charges $4Q, Q$ are separated by $1m$ in air. At what point on the line joining the charges is the electric field intensity zero?

Let electric field intensity at any point P which lie at a distance x m from 4Q be zero.
Electric field intensity $(E_1)$ due to $4Q$ at P
As direction of $E_1$ and $E_2$ are in opposite directions.
=> $\large\frac{1}{4 \pi \in _0} . \frac{4Q}{x^2}$
=>$\large\frac{1}{4 \pi \in_0 }. \frac{Q}{(1-x)^2}$
=> $\bigg( \large\frac{1-x}{x} \bigg)^2 =\frac{1}{4}$
$\large\frac{1-x}{x} =\frac{1}{3}$
$\large\frac{1}{x} $$-1 =\frac{1}{2} \large\frac{1}{x} =\frac{3}{2} x= \large\frac{2}{3}$$\;m$
Electric field intensity is zero at a point which lie at a distance $x= \large\frac{2}{3}$$m$ from $+4Q$ charge on the line joining two charges.