Two charged conducting spheres of radii $5 \ cm$ and $10 \ cm$ have equal surface charge densities. If the electric field on the surface of the smaller sphere is $E$,then the electric field on the surface of the larger sphere is

The linear charge densities of two infinitely long thin and parallel wires are $4 \ Cm^{-1}$ and $8 \ Cm^{-1}$,and the separation between them is $4 \ cm$. The electric field intensity at the midpoint on the line joining them is:

Two point charges $q_1$ and $q_2 (=q_1/2)$ are placed at points $A(0, 1)$ and $B(1, 0)$ as shown in the figure. The electric field vector at point $P(1, 1)$ makes an angle $\theta$ with the $x$-axis,then the angle $\theta$ is

Two electric charges $9e$ and $3e$ are placed at a distance $r$ from each other. The point where the electric field intensity is zero is at a distance of .......

$A$ point charge of $10\,\mu C$ is placed at the origin. At what location on the $X$-axis should a point charge of $40\,\mu C$ be placed so that the net electric field is zero at $x = 2\,cm$ on the $X$-axis?

$A$ circular wire loop of radius $1 \, cm$ carries a total charge $1 \times 10^{-6} \, C$ distributed uniformly over its length. If $0.01 \%$ of its length (circumference) is cut off, then the electric field at the centre of the loop due to the remaining wire is
$(\text{Take} \, \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \, \text{SI unit})$