Question

The electric field due to a short electric dipole at a distance $r$ from it, on its axial line is $E.$ The electric field on its axial line, at a distance $\frac{r}{2}$ will be equal to

​​​​​​​$[$0.77 Mark$]$

• A. $8E$
• B. $2E$
• C. $E$
• D. $4E$

Answer 1

The correct option is A $8E$

The electric field on its axial line due to a short dipole is given by,

$E=\frac{2kp}{r^3}(\text{where}k=\frac{1}{4\pi {\epsilon }_0})$

$\Rightarrow E\propto \frac{1}{r^3}$

So,

$\frac{E^{\prime }}{E}=\frac{r^3}{{\left(\frac{r}{2}\right)}^3}=8\Rightarrow E^{\prime }=8E$