Demonstrate that the potential of the field generated by a dipole with the electric moment `p` (fig) may be represented as `varphi = pr//4pi epsilon_(0) r^(3)`, where `r` is the redius vector. Using this expression, find the magnitude of the electric strength vector as a funcition of `r` and `theta`.

Two point charges q and -q are separated by the distance 2l . Find the flux of the electric field strength vector across a circle of radius R .

Two point charges q and -q are separated by a distance 2a. Evaluate the flux of the electric field strength vector across a circle of radius R.

Two point charges q and -q are separated by a distance 2a. Evaluate the flux of the electric field strength vector across a circle of radius R.

Find the electric field strength vector if the potentail of this field has the form varphi = ar , where is a constatn vector, and r is the radius vector of point of the field.

A dielectric ball is polarized uniformly and statically. Its polarization equals P . Taking into account that a ball ploarized is this way may be represented as a result of a small shift of all positive chagres of the dielectric relative to all negative charges, (a) find the electric field strength E inside the ball, (b) demonstrate that the field outside the ball is that of a dipole located at the centre of the ball, the potential of that field being equal to varphi = p_(0) r//4pi epsilon_(0) , where p_(0) is the electric moment of the ball, and r is the distance from its centre.

Determine the electric field intensity at any point P (r, theta ) due to an electric dipole.

If the electric potential in a region is represented as V = 2x + 3y - 4z .Then electric field vector will written as