# Physics Class 12 NCERT Solutions: Chapter 1 Electric Charges and Fields Part 4

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Q: 12. (A) Two insulated charged copper spheres A and B have their centers separated by a distance of. What is the mutual force of electrostatic repulsion if the charge on each is? The radii of A and B are negligible compared to the distance of separation.

(B) What is the force of repulsion if each sphere is charged the above amount, and the distance between them is halved?

(A) Charge on sphere A, Charge on sphere B,

Distance between the spheres,

Force of repulsion between the two spheres,

Where,

Free space permittivity

Therefore, the force between the two spheres is .

(B) After doubling the charge, charge on sphere A, Charge on sphere B,

The distance between the two spheres,

Therefore, the force between the two spheres is.

Q: 13. Suppose the spheres A and B in Exercise have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with second, and finally removed from both. What is the new force of repulsion between A and B?

Distance between the spheres, A and B,

Initially, the charge on each sphere,

When sphere A is touched with an uncharged sphere, C, amount of charge from A will transfer to sphere C. Hence, charge on each of the spheres, A and C, is. When sphere C with charge is brought in contact with sphere B with charge, total charges on the system will divide into two equal halves given as.

Each sphere will share half. Hence, charge on each of the spheres, C and B, is .

Force of repulsion between sphere A having charge and sphere B having charge

Therefore, the force of attraction between the two spheres is

Q: 14. Figure 1.33 shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charge. Which particle has the highest to mass ratio?

Opposite charges attract each other and same charges repel each other. It can be observed that particles and both move towards the positively charged plate and repel away from the negatively charged plate. Hence, these two particles are negatively charged. It can also be observed that particle moves towards the negatively charged plate and repels away from the positively charged plate. Hence, particle is positively charged.

The charge to mass ratio (emf) is directly proportional to the displacement or amount of deflection for a given velocity. Since the deflection of particle is the maximum, it has the highest charge to mass ratio.

Q: 15. Consider a uniform electric field . (A) What is the flux of this field through a square of on a side whose plane is parallel to the plane? (B) what is the flux through the same square if the normal to its plane makes a angle with the ?