The electric field in a region of space is given by $\vec{E} = (5\hat{i} + 2\hat{j}) \text{ N/C}$. Calculate the electric flux through a surface of area $2 \text{ m}^2$ lying in the $YZ$-plane.

Find the electric flux through the shaded face $BCGF$ of the cube,as shown in the figure.

If the radius of the spherical Gaussian surface is increased, then the electric flux due to a point charge enclosed by the surface

$A$ solid uncharged conducting sphere has a radius of $3a$ and contains a hollowed spherical region of radius $2a$. $A$ point charge $+Q$ is placed at a position a distance $a$ from the common center of the spheres. What is the magnitude of the electric field at the position $r = 4a$ from the center of the spheres as marked in the figure by $P$? $\left( {k = \frac{1}{{4\pi { \in _0}}}} \right)$

In the figure,a $+Q$ charge is located at one of the corners of the cube. What is the electric flux through the cube due to the $+Q$ charge?

$A$ point charge '$Q$' is placed at a point inside a hollow conducting sphere. Which of the following electric field patterns is correct?