Question

A negative charge is placed at some point of the joining the +Q charges at rest. The direction of motion of negative charge will depend upon the:
1) Position of negative charge alone
2) Magnitude of negative charge alone
3) Both on the magnitude and positive of negative charge
4) Magnitude of the positive charge

Answer 1

Hint: We have all played with magnets, when we bring the south pole of one magnet to the south pole of another magnet, we feel repulsion and when we bring the North Pole of one magnet to the north pole of another magnet, we see that the magnets attract to one another. A similar concept is used in this, in case of charges a positive-positive charge will repel and a positive-negative charge will attract. Apply this concept in the question and choose the correct option.

Complete step by step answer:
When a negative charge is placed in between two positive charges we see that the magnitude of both the positive charges affect the direction of a negative charge but this only true when both the positive charges are not equal. Suppose a positive charge has a value of +50C and another has +10C, the negative charge will go in the direction of a positive charge whose magnitude would be larger. In this case both the positive charges have the same magnitude so the magnitude of the positive charge won’t affect. Here, the position and only the position of the negative charge will affect its direction. If the position of the negative charge is nearer to a positive charge, it will go in the direction of the positive charge if the negative charge is in the middle it will stay in the middle.

Here just like the force of gravity there is a force that is applicable between the charges. The force is known as Coulomb's force. Coulomb's force is defined as the force applied by a one charge on another charge (both are at rest) separated by the square of the distance between them.
$F = K\dfrac{{{q_1}{q_2}}}{{{r^2}}}$
Here:
F = Force;
K = Proportionality constant.
${q_1}$= Charge 1.
${q_2}$= Charge 2.
Here the two positive charges +Q are attracting the negative charge -q and the force applied by the charges is inversely proportional to the square of the distance between them.
\[F \propto \dfrac{1}{{{r^2}}}\];
So that means the force will increase if the distance between two charges decreases and the vice versa is also true.
Final Answer: A negative charge is placed at some point of the joining the +Q charges at rest. The direction of motion of negative charge will depend upon the position of negative charge alone i.e Option A.
Note: Here most students make the mistake of assuming that the two positive charges are different, carefully read the question. Apply the concept of negative-negative and positive-positive repulsion and negative-positive attraction.