will the test charge move along tangent to the curve at point A ( in the following figure)

Will a positive test charge placed at point A move along the electric field line (i.e curved path ) or go straight in the direction of tangent at point A?

• What do you think and please give a reason for your answer? Jan 19, 2017 at 7:53
• @Farcher As far as I know net Force will act along tangent to point A. So I guess it should follow this path i.e it should go along the tangent.
– rock
Jan 19, 2017 at 9:30

The diagram tells you that the force on a positive charge will be along a tangent to the electric field line at point $A$ and will be directed in the same sense as the arrow on the electric field line.
This gives you the direction of the acceleration and hence the rate of change of velocity of the charge.

If at point $A$ the charge is at rest then the charge will start to move along the tangent.
However in general although you know the direction of the force on the test charge, its acceleration and its rate of change of velocity unless you know the velocity of the charge you cannot predict which way it will continue to move.
That being said that even though you can predict the direction in which a stationary charge will start to move it will not continue moving along the electric field line unless the electric field is uniform.

• ok lets assume a test charge is at rest at point A. Now I wonder will it reach the negative charge present on the right or not?
– rock
Jan 19, 2017 at 12:41

No.

If the particle is not mass-less, its inertia won't let it change direction easily, that is, it will drift away from the field line you have separated, getting as much closer to a linear, constant-velocity motion as possible, at the first law of Newton says.

• So you are saying that it will not reach the negative charge present at right hand side?
– rock
Jan 19, 2017 at 12:42
• @rock Not that! It will eventually reach there. but the path is a little bit tending to diverge out. it may rotate around the negative charge a little bit so that it finally reaches it. But The path is not that of field lines.
– AHB
Jan 19, 2017 at 12:52