Question

An electric potential field is produced by point charges 1 mC and 4 mC located at (-2,1,5) and 52 and (1,3,1) respectively. The energy stored in the field is

Answer 1

Given,

Point charge $(q_1)=1mC$

$q_2=4mC$

Let co-ordinates be P and B are (-2,1,5) and (1,3,1)

$r_1=-2\hat{i}+\hat{j}+5\hat{k}$

$r_2=\hat{i}+3\hat{j}+\hat{k}$

$\Rightarrow \overrightarrow{d}=r_2 - r_1$

$\Rightarrow \overrightarrow{d}=\hat{i}+3\hat{j}+\hat{k} +2\hat{i}-\hat{j}-5\hat{k}$

$\Rightarrow \overrightarrow{d}=3\hat{i}+2\hat{j}-4\hat{k}$

$|d|=\sqrt{3^2+2^2+4^2}$

$=\sqrt{9+4+16}$

$=\sqrt{29}$

Hence, the required stored energy,

$U=\frac{q_1q_2}{4\pi \epsilon_o d^2}$

Now, substituting the values,

$\Rightarrow U = \frac{9\times 10^9\times1\times 10^{-3}\times 4\times 10^{-3}}{29}$

$\Rightarrow U = 1.24\times 10^{3}J$