# NCERT Physics Class12 Exampler Chapter-2 Electrostatic Potential and Capacitance Part-8

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Q.25 Two point charges of magnitude and are placed at and, respectively. Find the equation of the equipotential surface where the potential is zero.

Solution:

Let the plane be at a distance from the origin. The potential at the point is

If this is to be zero.

Or,

Or,

The equation is that of a plane x=0.

Q. 26 A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage as where .A similar capacitor with no dielectric is charged to. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.

Solution:

Let the final voltage be If is the capacitance of the capacitor without the dielectric, then the charge on the capacitor is

The capacitor with the dielectric has a capacitance. Hence the charge on the capacitor is

The initial charge on the capacitor that was charged is

From the conservation of charges,

Or,

Volts

As U is Positive

Q.27 A capacitor is made of two circular plates of radius each. Separated by a distance, the capacitor is connected to a constant voltage. A thin conducting disc of radius and thickness is placed at a centre of the bottom plate. Find the minimum voltage required to lift the disc if the mass of the disc is.

Solution:

When the disc is in touch with the bottom plate, the entire plate is equipotential. A change’ is transferred to the disc.

The electric field on the disc is

The force acting on the disc is

If the disc is to be lifted, then

Q.28 (a) in a quark model of elementary particles, a neutron is made of one up quarks [change e] and two down quarks [charges e]. Assume that they have a triangle configuration with side length of the order of. Calculate electrostatic potential energy of neutron and compare it with its mass.

(b) Repeat above exercise for a proton which is made of two up and one down quark.

Solution: