The electric field in a region is uniform and is given by $\vec{E} = a \hat{i} + b \hat{j} + c \hat{k}$. The electric flux associated with a surface of area $\vec{A} = \pi R^2 \hat{i}$ is:

$A$ long straight wire of radius $1 \, mm$ has a uniform charge distribution. The charge per $cm$ length of the wire is $Q \, Coulombs$. $A$ cylinder of radius $50 \, cm$ and length $1 \, m$ encloses the wire symmetrically. The total flux passing through the surface of the cylinder is ..........

The figure shows the electric field lines for a system of two charges. Choose the correct option regarding the electric field intensity at points $A$,$B$,and $C$.

$A$ 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 $P$? $\left( {k = \frac{1}{{4\pi { \in _0}}}} \right)$

The electric field in a region of space is given by $\overrightarrow E = E_0 \hat i + 2E_0 \hat j$,where $E_0 = 100 \, N/C$. The flux of the field through a circular surface of radius $0.02 \, m$ parallel to the $Y-Z$ plane is nearly:

What is called a Gaussian surface?