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

Download PDF of This Page (Size: 214K)

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.

Image of Circuit in question

Image of Circuit in Question

Image of Circuit in question

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:

Image of Circuit

Image of Circuit

Image of Circuit

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:

Image of Potential Radius Disc

Image of Potential Radius Disc

Image of Potential Radius Disc

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

Solution:

Locus of zero potential

Locus of Zero Potential

Locus of zero potential

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:

Unstable equilibrium

Unstable Equilibrium

Unstable equilibrium

is an equilibrium point.

At

, which is .

Hence, unstable equilibrium.