A uniform ring charge of radius  carries a total charge . Which one of the following options correctly quantifies the magnitude of the force on a point charge of strength  kept at the center of the ring?

( is the permittivity of the medium)

Which one of the following figures represents the radial electric field distribution  caused by a spherical cloud of electrons with a volume charge density,  for  (both  are positive and  is the radial distance) and  for  ?

Let  be the unit radial vector in the spherical co-ordinate system. For which of the following value(s) of , the divergence of the radial vector field  is independent of  ?

In the  coordinate system, three point-charges , and  are located in free space at , and , respectively. The value of  for the electric field to be zero at  is ________(rounded off to 1 decimal place).

A positive charge of 1nC is placed at (0, 0, 0.2) where all dimensions are in metres. Consider the x - y plane to be a conducting ground plane. Take . The Z component of the E field at (0, 0, 0.1) is closest to

Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed

Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +Q is placed at a distance of d from both sheets. The net force on the charge is, where K is given by

A perfectly conducting metal plate is placed in x-y plane in a right-handed coordinate system. A charge of  coulombs is placed at coordinate (0,  0, 2).  is the permittivity of free space. Assume   to be unit vectors along x, y and z axes, respectively. At the coordinate, the electric field vector  (Newtons/Columbs) will be

A solid sphere made of insulating material has a radius R and has a total charge Q distributed uniformly in its volume. What is the magnitude of the electric field intensity, E, at a distance r (0<r<R) inside the sphere?

An inductor designed with 400 turns coil wound on an iron core of  cross sectional area and with a cut of an air gap length of 1mm. The coil is connected to a 230 V, 50 Hz AC supply.  Neglect coil resistance, core loss, iron reluctance and leakage inductance

The current in the inductor is

An inductor designed with 400 turns coil wound on an iron core of  cross sectional area and with a cut of an air gap length of 1mm. The coil is connected to a 230 V, 50 Hz AC supply.  Neglect coil resistance, core loss, iron reluctance and leakage inductance

The average force on the core to reduce the air gap will be

The electric field  (in volts/metre) at the point (1, 1, 0) due to a point charge of +1µC located at (−1, 1, 1) (coordinates in metres) is  

An infinite number of charges, each equal to ‘q’ are placed along the x=1, x=2 , x=4, x=8 , x=16 and so on. Find the potential and electron field at point x=0, due to these systems of charges.

Determine the electric field intensity at the point p for the arrangement shown in figure above