A point charge q moves from A to B along a parabolic path (AB is latus rectum). Electric field is along x−axis. The work done by the field is
At latus rectum.
The equation of the parabola is y2=4ax
Therefore, The focal length =a
Therefore, the length of the latus ractum =4a
As the particle is moving along the latus rectum,
Total displacement in the direction of electric field, d=4a
Work done by electric field, w=qE.d=qE.4a=+4qEa
Hence, work done in electric field is +4qEa