(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.
Answers
a) Let us consider that initially the rest charge is in the stable equilibrium .
When the rest charge is taken away from the null point (i.e) E=0E=0 , in any direction , it must experience a restoring force towards the null point.
b) The middle point of the line joining two like charges is a null point.
If we take a test charge slightly away from the point along the line, the restoring force. will try to bring it back to the centre.
If we take the rest change normal to the line, the net force on the test charge takes it further away from the null point.
Therefore the equilibrium is not stable.
(a) it will undergo a restore force to a null point where the electrical field is zero
(b) Therefore, the charge is unstable since equilibrium stability demands that force be restored in every direction.
Explanation:
(a) Let the Test Charging balance be stable. When a test charge is in equilibrium and shifted in some direction from its location, it will undergo a restore force to a null point where the electrical field is zero. All field lines close to null point are pointed inward to null point. There is still a net inward flow of electrical field across the null point, via a closed wall. According to the law of Gauss, the flow of electric field across a surface that does not contain any charge is zero. Hence the check charge balance can be positive.
(b) Around a certain distance are mounted two charges of the same magnitude and same number. The midpoint of the charges connecting line is the null point. If a charged check is passed down the line it will feel a restore power. If normal to the connecting line is displaced, otherwise the net force eliminates it from the null point. Therefore, the charge is unstable since equilibrium stability demands that force be restored in every direction.
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(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.
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Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point of the condfiguration. Show that the equilibrium of the test charge is necessarity unstable.
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