Consider a circular loop that is uniformly charged and has a radius $R = a \sqrt{2}$. Find the position along the positive $z$-axis of the Cartesian coordinate system where the electric field is maximum,assuming the ring is placed in the $xy$-plane at the origin.

An infinitely long uniformly charged string is placed along the $z-$axis. Its linear charge density is $\lambda$. $A$ point charge $q$ is moved from position $(a, 0, 0)$ to $(2a, 0, 0)$. The work done by the external agent is:

Four charges $q, 2q, -4q$ and $2q$ are placed in order at the four corners of a square of side $b$. The net field at the centre of the square is

Consider two points $1$ and $2$ in a region outside a charged sphere. These two points are not very far away from the sphere. If $\overrightarrow{E}$ and $V$ represent the electric field vector and the electric potential respectively,which of the following is not possible?

The variation of electric field along the $Z$-axis due to a uniformly charged circular ring of radius '$a$' in the $XY$ plane is shown in the figure. The value of coordinate $M$ will be

$A$ thin half ring of radius $35 \text{ cm}$ is uniformly charged with a total charge of $Q$ coulomb. If the magnitude of the electric field at the centre of the half ring is $100 \text{ V/m}$,then the value of $Q$ is . . . . . . $\text{nC}$. ($\epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2/\text{Nm}^2$ and $\pi = 3.14$)