# NCERT Physics Class12 Exampler Chapter-2 Electrostatic Potential and Capacitance Part-9

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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.