# NCERT Physics Class12 Exemplar Chapter-2 Electrostatic Potential and Capacitance Part-9 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Q. 29 Two metal spheres, one of radius and the other of radius , both have same surface charge density . They are brought in contact and separated. What will be new surface charge densities on them?

Solution:

Before contact:

After contact:

,

They will be at equal potentials:

=

And

And .

Q. 30In the Circuit, shown in figure.

Initially is closed and is open. What are the charges on each capacitors?

Then was opened and was closed (order is important) , what will be the charge on each capacitor now?

Solution:

Initially: and

And

And

Later:

With

And

Q. 31 Calculate potential on the axis of a disc of radius due to a charge uniformly distributed on its surface.

Solution:

Q. 32 Two charges and are placed at and respectively. Find Iocus of points where the potential a zero.

Solution:

Thus, to have total potential zero, and must have opposite signs. Squaring and simplifying, we get.

This is the equation of a sphere with centre at

Note: if Then , which is a plane through mid-point.

Q. 33 Two charges each are separated by distance . A third charge is kept at mid-point . Find potential energy of as a function of small distance from due to charges. Sketch P. E. v/s and convince yourself that the charge at is in an unstable equilibrium.

Solution:

is an equilibrium point.

At

, which is .

Hence, unstable equilibrium.