Question

(Figure 1) Consider three plastic balls (A, B, and C), each carrying a uniformly distributed charge equal to either +Q, -Q or zero, and an uncharged (neutral) copper ball (D). A positive test charge (T) experiences the forces shown in the figure when brought very near to the individual balls. The test charge T is strongly attracted to A, strongly repelled from B, weakly attracted to C, and strongly attracted to D.

What is the nature of the force between balls A and B?

What is the nature of the force between balls A and B?

	strongly attractive
	strongly repulsive
	weakly attractive
	neither attractive nor repulsive

Answer 1

Concepts and reason

The concept required to solve the given problem is nature of electrostatic force between two charges.

Find out the nature of force between balls A and B by identifying the sign of each charge with the help of nature of force on test charge due to these two charges individually.

Fundamentals

Properties of Coulomb force between two charges: Two unlike charges attract each other whereas two like charges repel each other.

According to Coulomb’s law, the magnitude of electrostatic force between two charges is given as follows:

$F = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{q_1}{q_2}}}{{{r^2}}}$

Here, q₁ and q₂ are charges, ${\varepsilon _0}$ is the permittivity of free space, and r is the distance between the charges.

According to the properties of Coulomb force, two unlike charges attract each other, while two like charges repel each other.

As the positive test charge T is strongly attracted to A, therefore, the charge on the ball A is negative.

As the positive test charge T is strongly repelled by B, therefore, Ball B must be positive, since two like charges repel each other.

The charges on the ball A is negative while charges on the ball is positive. As opposite charges attract each other, while two like charges repel each other, therefore, the interaction between negative ball A and very positive ball B is strongly attractive. Hence, the nature of force between balls A and B is strongly attractive.

Ans:

The nature of the force between ball A and ball B is strongly attractive.