(a) Derive an expression for the electric field at any point on the equatorial line of an electric dipole.
(b) Two identical point charges, q each, are kept 2m apart in air. A third point charge Q of unknown magnitude and sign is placed on the line joining the charges such that the system remains in equilibrium. Find the position and nature of Q.
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The electric field at the equatorial line of an electric dipole will be as follows.
1)Let's assume we have a dipole with charge Q and q.
2)Since it is a dipole then let's assume that Q is positive while q is negative .
3)Now to test the electric field at the equatorial line joining the two charges we need to put a test charge their.
4)Electric field on our test charge due to the charge Q will be Q/4 .PI. EPSILON R^2,where R is the distance between them.
5)Similarly the electric field on our test charge due to the charge q will be q/4.pi.epsilon.R^2
6)We observe that if the two charges are of equal magnitude then the electric field at the equatorial line of the dipole will be zero.
B)Similarly when a test charge is placed on a dipole separated by a distance of 2m such that the arrangement is not disturbed then the following is observed
1)The test charge Q will be placed at a distance of 1m which is exactly the midpoint between the two charges.
This happens because at the midpoint between two charges the electric field due to both the charges will cancel each other out and hence the charge will experience no force when it is kept at this point .