CBSE Class 12-science Answered

(a)Electric field intensity at any point outside a uniformly charged spherical shell:

Consider a thin spherical shell of radius R and with centre O. Let charge + q be uniformly distributed over the surface of the shell.

Let P be any point on the Gaussian sphere S₁ with centre O and radius r, as shown in the following figure.

According to Gauss's law, we can write the flux through ds as:

At any point on the surface of the shell, r = R

Field lines when charge density of the sphere is positive

Field lines when charge density of the sphere is negative

(b) Diameter of the sphere = 2.5 m

Radius of the sphere,

Charge density,

(i) Total charge,

(ii) Total electric flux,

Or

(a) The figure given below shows an electric dipole of charges +q and -q which are separated by distance 2a.

Expression for the torque: The above arrangement forms a couple. The couple exerts a torque which is given by,

=Force x Perpendicular distance between the two forces

=qE x 2a.sin

=pE.sin, where p=qx2a=Dipole moment.

Since the direction of torque is perpendicular to we can rewrite the above equation as,

=

(b) The work done will be equal to the potential energy of the system