Question

a test charge q is placed in the electric field of a source charge Q. test charge will not follow path of electric field if its velocity is?

Answer 1

Explanation:

If the test charge corresponds to a massive particle, the path actually traced out differs from the actual direction of the electric field line, due to inertia.

Assume for illustration that the electric field E⃗ E→ curves in space, i.e. deviates from a straight line. As this test charge particle moves an infinitesimal distance along the direction of E⃗ E→, inertia of motion dictates that it would tend to move along that direction itself, even as the E⃗ E→ for the next infinitesimal element changes direction. Thus, for the second infinitesimal path length, the problem becomes a case of initial velocity along one direction, and the instantaneous acceleration a⃗ =qE⃗ /ma→=qE→/m pointing in a slightly different direction. It is easily imaginable that the trajectory for this infinitesimal path length is not exactly along the direction of E⃗ E→ itself. The same argument can be readily extended to subsequent infinitesimal length elements.