# Physics Class 12 NCERT Solutions: Chapter 1 Electric Charges and Fields Part 11 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Q: 31. It is now believed that protons and neutrons (Which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks, the so called ‘up’ quark (denoted by u) of charge together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and neutron.

A proton has three quarks. Let there be n up quarks in a proton, each having a charge of

Charge due to up quarks

Number of down quarks in a proton

Each down quark has a charge of .

Charge due to

Total charge on a proton

Number of up quarks in a proton,

Number of down quarks in a proton

Therefore, a proton can be represented as

A neutron also has three quarks. Let there be n up quarks in a neutron, each having a charge of .

Charge on a neutron due to n up quarks

Number of down quarks is , each having a charge of .

Charge on a neutron due to down quarks

Total charge on a neutron

Number of up quarks in a neutron,

Number of down quarks in a neutron

Therefore, a neutron can be represented as. .

Q: 32. (A) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point of the configuration. Show that the equilibrium of the test charge is necessarily unstable.

(B) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart

(A) Let the equilibrium of the test charge be stable. If a test charge is in equilibrium and displaced from its position in any direction, then it experiences a restoring force towards a null point, where the electric field is zero. All the field lines near the null point are directed inwards towards the null point. There is a net inward flux of electric field through a closed surface around the null point. According to Gauss՚s law, the flux of electric field through a surface, which is not enclosing any charge, is zero. Hence, the equilibrium of the test charge can be stable.

(B) Two charges of same magnitude and same sign are placed at a certain distance. The mid-point of the joining line of the charges is the null point. When a test charged is displaced along the line, it experiences a restoring force. If it is displaced normal to the joining line, then the net force takes it away from the null point. Hence, the charge is unstable because stability of equilibrium requires restoring force in all directions

33: A particle of mass and charge enters the region between the two charged plates initially moving along x-axis with speed vx (like particle 1 in Fig. 1.33) . The length of plate is L and a uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is

Compare this motion with motion of a projectile in gravitational field discussed in Section of Class XI Textbook of Physics.

Charge on a particle of mass

Velocity of the particle

Length of the plates

Magnitude of the uniform electric field between the plates

Mechanical force,

However electric force,

Therefore, acceleration,

Time taken by the particle to cross the field of length L is given by,

In the vertical direction, initial velocity,

According to the third equation of motion, vertical deflection s of the particle can be obtained as,

Hence, vertical deflection of the particle at the far edge of the plate is . This is similar to the motion of horizontal projectiles under gravity.