Question

An electret is similar to a magnet, but rather than being permanently magnetized, it has a permanent electric dipole moment. Suppose a small electret with electric dipole moment $1.0\times {10}^{-7}Cm$ is $25cm$from a small ball charged to $+25nC$, with the ball on the axis of the electric dipole. What is the magnitude of the electric force on the ball?

Short answer

The electric force on the ball is$9.216\times {10}^{-3}N$.

Step-by-step solution

Given information

Given the electric dipole of charge $25nC$with a dipole moment of ${10}^{-7}Cm$separated b distance$25cm$.

Explanation

Electric field due to a dipole:

$$\begin{gathered} E=\frac{2p}{4\pi {\epsilon }_0{r}^3} \\ E=\frac{9\times {10}^9\times 2\times 1\times {10}^{-7}}{{25}^3\times {10}^{-6}} \\ E=1.152\times {10}^{5}N/C \end{gathered}$$

The electric force on the ball:

$$\begin{gathered} E=\frac{F}{q} \\ F=Eq \\ F=\left(1.152\times {10}^{5}N/C\right)\left(1.0\times {10}^{-7}Cm\right) \\ F=9.216\times {10}^{-3}N \end{gathered}$$

The electric force on the ball is$9.216\times {10}^{-3}N$