Question

What is the electric intensity at a point in between two equal and like charges

Answer 1

Let us first derive the formula for acceleration of a particle with charge ‘q’ and mass ‘m’ in an electric field of strength ‘E’

We know, F=m*a (force on the particle)

We also have : E=F/q which gives F=q*E

So we now have q*E=m*a and that gives us the formula for acceleration of a particle which is:

a=(q*E)/m

Therefore, if the electric field in consideration is a uniform one i.e if the field strength is constant throughout, both the particles will have equal acceleration as m and magnitude of q are equal for both charges and E is constant. (Important to note that they will be moving in exactly opposite directions)

However, if the field is that of a point charge, then the case would be different.

For a point charge with charge magnitude Q, electric field strength at a distance r is given by:

E=(k*Q)/r^2 , where k is the electrostatic constant.

This shows, for a given point charge, electric field strength decreases as distance from the point charge increases.

The acceleration for a particle with charge ‘q’ and mass ‘m’ in an electric field due to a point charge Q at a distance ‘r’ from Q is:

a=(q*k*Q)/(m*r^2) (from a=(q*E)/m)

This shows, from the two charges in consideration, the charge whose distance will be decreasing i.e the charge that will be travelling towards Q will be accelerating more as q(magnitude) and m are equal for both charges and k is constant, whereas r and in turn r^2 varies.

For a positive point charge, electric field is radially outside, so of the two charges in consideration, the negative one will travel towards the point charge (distance- r decreasing) and the positive one will travel away. From the last equation, negative one will have a greater acceleration.

For a negative point charge, the case is exactly opposite of the one for a positive point charge. The electric field will be radially inside, so the positive one will travel towards the point charge and the negative one will travel away. Here, the positive one will have higher acceleration.

I hope this helps!