Question

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

• A. $1.50\times {10}^{-3}\text{N/C}$
• B. $2.25\times {10}^{-3}\text{N/C}$
• C. $1.88\times {10}^{-3}\text{N/C}$
• D. $2.88\times {10}^{-3}\text{N/C}$

Answer 1

The correct option is D $2.88\times {10}^{-3}\text{N/C}$

Given:
Distance of charges from centre of dipole, $l=1\text{mm};$

Distance of point $\text{P}$ from centre of dipole, $x=5.001\approx 5\text{m};$

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

Here, we can see that $l<<x$

Therefore, the net electric field due to a dipole at an axial point is given by

$|{\overrightarrow{E}}_{ax}|=\frac{2k|\overrightarrow{p}|}{x^3}=\frac{2k\left(q2l\right)}{x^3}=\frac{4kql}{x^3}$

$\Rightarrow |{\overrightarrow{E}}_{ax}|=\frac{4\times 9\times {10}^9\times 10\times {10}^{-9}\times 1\times {10}^{-3}}{5^3}$

$\Rightarrow |{\overrightarrow{E}}_{ax}|=2.88\times {10}^{-3}\text{N/C}$

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