Question

Question 1.32: (a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable. (b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

Class 12 - Physics - Electric Charges And Fields Electric Charges And Fields Page-50

Answer 1

needlework you have to observe the laws of the day h is a good day at the moment and I have a great day at today so

Answer 2

(a) Let us assume that a radial electric field is present with origin as centre . the E is zero at origin and a small test charge q₀ is placed at origin. force on test charge is zero because electric field is assumed by us is zero.
as you know, F =qE = 0
but the test charge is displaced a little , the electric field will drift it further away so charge is in unstable equilibrium.

(b) A test charge place at midpoint of equal charges is in stable equilibrium, for lateral displacement.
initially at midpoint position of test charge, two repulsion forces on test charges are equal and opposite.
e.g., FA = FB , so it is in equilibrium.
but on displacing q₀ close to one of the charge, one of the force become stronger and pushes the charge towards another.
FA > FB , $\bf{so\:q_0\:moves\:towards\:B}$
this is what ? of course equilibrium of charges are necessarily unstable.