Question

The distance between the two charges $+q$ and $-q$ of a dipole is $r$ . The intensity at a point on the axial line at a distance $x$ from the centre of dipole is proportional to :

• A. $\frac{q}{x^2}$
• B. $\frac{qr}{x^2}$
• C. $\frac{q}{x^3}$
• D. $\frac{qr}{x^3}$

Answer 1

The correct option is D $\frac{qr}{x^3}$

The electric field at the distance $x$ from the center of the dipole having distance $r$ along the axis is given as

$E_{+q}=\frac{kq}{\left(x-\frac{r}{2}\right)}$

$E_{-q}=\frac{kq}{\left(x+\frac{r}{2}\right)}$

The net electric field is given as

$E=E_{+q}-E_{-q}$

$E=\frac{kq}{{\left(x-\frac{r}{2}\right)}^2}-\frac{kq}{{\left(x+\frac{r}{2}\right)}^2}$

$E=\frac{2kqxr}{{\left(x^2-{\left(\frac{r}{2}\right)}^2\right)}^2}$

For $x>>r$ then we can neglect$$r$$in the above equation and we get

$E=\frac{2kqxr}{x^4}$

$E=\frac{2kqr}{x^3}$