Question

Find the net electric field at an equatorial point $\text{P}$ of a dipole as shown in figure.

• A. $1.8\times {10}^{-3}\text{N/C}$
• B. $2.8\times {10}^{-3}\text{N/C}$
• C. $3.8\times {10}^{-3}\text{N/C}$
• D. $4.8\times {10}^{-3}\text{N/C}$

Answer 1

The correct option is B $2.8\times {10}^{-3}\text{N/C}$

Given:
Distance of charges from centre of dipole, $l=1\text{mm}={10}^{-3}\text{m}$

Distance of point $\text{P}$ from centre of dipole, $x=4\text{m}$

Magnitude of charge, $q=10\text{nC}$

Here, $x>>l$, therefore, net electric field due to a dipole at an equatorial point is given by

$|{\overrightarrow{E}}_{eq}|=\frac{k|\overrightarrow{p}|}{x^3}=\frac{2kql}{x^3}$

$\Rightarrow |{\overrightarrow{E}}_{eq}|=\frac{2\times 9\times {10}^9\times 10\times {10}^{-9}\times 1\times {10}^{-3}}{4^3}$

$\Rightarrow |{\overrightarrow{E}}_{eq}|=2.8\times {10}^{-3}\text{N/C}$

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