As shown in the figure below, two concentric conducting spherical shells, centered at r = 0 and having radii r = c and r= d are maintained at potentials such that the potential V(r) at r = c is  and V(r) at r = d is . Assume that V(r) depends only on r, where r is the radial distance. The expression for V(r) in the region between r = c and r = d is

The vector function expressed by

represents a conservative field, where , ,  are unit vector along x, y and z directions, respectively. The values of constants , ,  are given by:

In cylindrical coordinate system, the potential produced by a uniform ring charge is given by , where f is a continuous function of r and z. Let  be the resulting electric field. Then the magnitude of

Two electric charges q and -2q are placed at (0,0) and (6,0) on the x-y plane. The equation of the zero equipotential curve in the x-y plane is

Match the following:

If  is the electric field intensity,  is equal to

A point charge of +1nC is placed in a space with a permittivity of  as shown in Figure. The potential difference  between two points P and Q at distances of 40 mm and 20 mm respectively from the point charge is

Given the potential function in free space to be  volts, the magnitude (in volts/metre) and the direction of the electric field at a point (1, -1, 1), where the dimensions are in metres, are

In a uniform electric field, field lines and equipotentials

If v, w, q stand for voltage, energy and charge, then v can be expressed as

A spherical conductor of radius ‘a’ with charge ‘q’ is placed concentrically inside an uncharged and unearthed spherical conducting shell of inner and outer radii  respectively. Taking potential to be zero at infinity, the potential at any point P within the shell  will be:        

A hollow conductor is at a potential V. The potential at any point inside the hollow is V.  ( True=1, False=0)

An electrostatic potential is given by  volts in the rectangular co-ordinate system. The magnitude of the electric field at ,  is _____________ V/m