Question

Electric field in a region is given by $E=-4x\hat{i}+6y\hat{j}$, find the charge enclosed in cube of side $1$ m oriented as shown in figure.

• A. $2{\epsilon }_o$
• B. Zero
• C. ${\epsilon }_o$
• D. $6{\epsilon }_o$

Answer 1

The correct option is A $2{\epsilon }_o$

$\overrightarrow{E}=-4x\hat{i}+6y\hat{j}$

$2\oint \overrightarrow{E}.\overrightarrow{ds}=\frac{Q_{enc}}{{\epsilon }_0}$

$\Rightarrow 2[-{\int }_0^{1}4xdx+{\int }_0^{1}6ydy]=\frac{Q_{enc}}{{\epsilon }_0}$

$\Rightarrow 2[-\frac{4}{2}+\frac{6}{2}]=\frac{Q_{enc}}{{\epsilon }_0}$

$\Rightarrow Q_{enc}=2{\epsilon }_0$