NCERT Physics Class12 Exemplar Chapter-2 Electrostatic Potential and Capacitance Part-8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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:

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