A point charge $q$ moves from $A$ to $B$ along a parabolic path ( $A B$ is latus rectum). Electric field is along $x -$ axis. The work done by the field is

- q E a

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+ q E a

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- 2 q E a

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4 q E a

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Solution

The correct option is D $4 q E a$
At latus rectum.
The equation of the parabola is $y^{2} = 4 a x$
Therefore, The focal length $= a$
Therefore, the length of the latus ractum $= 4 a$
As the particle is moving along the latus rectum,

Total displacement in the direction of electric field, $d = 4 a$

Work done by electric field, $w = q E . d = q E .4 a = + 4 q E a$

Hence, work done in electric field is $+ 4 q E a$

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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

A point charge $q$ moves from $A$ to $B$ along a parabolic path ( $A B$ is latus rectum). Electric field is along $x -$ axis. The work done by the field is