Question

Find the dipole moment of a system where the potential $2.0\times {10}^{-5}V$ at a point P, $0.1m$ from the dipole is $3.0\times {10}^4$. (Use $\theta ={30}^o)$.

• A. $2.57\times {10}^{-17}Cm$
• B. $1.285\times {10}^{-15}Cm$
• C. $1.285\times {10}^{-17}Cm$
• D. $2.57\times {10}^{-15}Cm$

Answer 1

The correct option is A $2.57\times {10}^{-17}Cm$

The potential at a distance r due to dipole is $V=\frac{1}{4\pi {ϵ}_0}\frac{\overrightarrow{p}.\hat{r}}{r^2}$ where $\overrightarrow{p}=$ dipole moment.

or $V=\frac{1}{4\pi {ϵ}_0}\frac{p\cos \theta }{r^2}$

or $p=\frac{4\pi {ϵ}_{0}V{r}^2}{\cos \theta }=\frac{4\pi \times 8.85\times {10}^{-12}\times 2\times {10}^{-5}\times (0.1{)}^2}{\cos 30}=2.57\times {10}^{-17}Cm$