Question

An electrical charge $2\times {10}^{-8}$ C is placed at the point (1, 2, 4 )m. At the point (4, 2, 0) m, the electric

• A. potential will be 36 V
• B. field will be along y-axis
• C. field will increase if the space between the points is filled with a dielectric
• D. All of the above

Answer 1

The correct option is A potential will be 36 V

Here, charge$q=2\times {10}^{-8}C$ and $r=\sqrt{(1-4{)}^2+(2-2{)}^2+(4-0{)}^2}=\sqrt{25}=5m$

and $\hat{r}=\frac{\overrightarrow{r}}{r}=\frac{1}{5}\left[\right(1-4)\hat{i}+(2-2)\hat{j}+(4-0\left)\hat{k}\right]=\frac{1}{5}[-3\hat{i}+4\hat{k}]$

Thus, potential $V=\frac{1}{4\pi {ϵ}_0}\frac{q}{r}=9\times {10}^9\times \frac{2\times {10}^{-8}}{5}=36V$

Electric filed $\overrightarrow{E}=\frac{1}{4\pi {ϵ}_0}\frac{q}{r^2}\hat{r}=9\times {10}^9\times \frac{2\times {10}^{-8}}{5^2}.\frac{1}{5}[-3\hat{i}+4\hat{k}]=1.44[-3\hat{i}+4\hat{k}]$

Thus, the field will along $x-z$ plane.

If space between points is filled by dielectric, the filed becomes $E^{\prime }=E/k$ where $k=$ dielectric constant. since, $k>1$ so filed will decrease.