Question

Two short electric dipoles of moment $P$ and $27P$ are placed as shown below. If at the point $O$ the electric field is zero between the dipoles, then the distance of the point $O$ from the centre of first dipole is

• A. $6\text{cm}$
• B. $8\text{cm}$
• C. $4\text{cm}$
• D. $2\text{cm}$

Answer 1

The correct option is D $2\text{cm}$

Let the electric field at point $O$ due to dipole $\left(1\right)$ be $E_1$ and due to dipole $\left(2\right)$ be $E_2$.

At $O$,
$E_1-E_2=0\Rightarrow E_1=E_2$

Let point O be $x$ distance away from dipole $\left(1\right)$. Then it will be $(8-x)$ distance away from dipole $\left(2\right)$

For a short dipole, electric field at axial line of dipole is given by
$|\overrightarrow{E}|=\frac{2k|\overrightarrow{p}|}{x^3}$

for electric dipole $\left(1\right)$,

$E_1=\frac{2kP}{x^3}$

and for electric dipole $\left(2\right)$,

$E_2=\frac{2k\times 27P}{(8-x{)}^3}$

Since, $E_1=E_2$

$\Rightarrow \frac{2kP}{x^3}=\frac{2k\times 27P}{(8-x{)}^3}$

$\Rightarrow \frac{1}{x^3}=\frac{27}{(8-x{)}^3}$

$\Rightarrow (8-x{)}^3=3^3\times x^3$

$\Rightarrow 8-x=3x$

$\Rightarrow x=2\text{cm}$

So, option $\left(a\right)$ is correct.