Electric Charges And Fields

Answer (a) zero

The line density in electric field lines give the information of strength or magnitude of an electric field. Here line density in electric field lines at and is same. So the electric filed at and will be same.

Answer (c) At a distance from

Answer (c) 10 J

A system of three charges is in equilibrium when the net force on each charge is zero. Let us consider two equal charges placed at the positions and on the x-axis, with the charge placed at the origin.

For charge to be in equilibrium, the net force acting on it due to charges needs to be zero. The forces exerted on by are equal in magnitude and opposite in direction. If is the force due to the charge at and is the force due to the charge at , then .

By Coulomb's Law, the force between two point charges is given by:

Here, the forces can be represented as:

Since and are equal and acting oppositely, the charge does not move.

For charge Q at -a and at a to be in equilibrium due to charge an additional condition is needed. The forces on these charges Q must be balanced. The force on charge at due to central charge is:

The force between charges at positions and should be equal and opposite to F_q for equilibrium condition:

Setting :

Solving for , we have:

Thus, for the system to be in equilibrium, the charge should be: