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  • A test charge q is made to move in the electric field of a point charge Q along two different closed paths. The first path has sections along and perpendicular to lines of the electric field,

A test charge q is made to move in the electric field of a point charge Q along two different closed paths. The first path has sections along and perpendicular to lines of the electric field, the second path is a rectangular loop of the same area as the first loop. How does the work done compare in the two cases?

Answers (1)

Explanation:-

 

In this path:

Along the section parallel to the electric field, work is done because the displacement is in the direction of the electric field. Along the section perpendicular to the electric field, no work is done, since E?⋅dr?=0 (the electric field is perpendicular to the displacement).

Even though some parts of the path involve work being done, since the total path is closed (starting and ending at the same point), the work done over the entire closed path is still zero. This is a property of conservative forces (such as the electric field of a point charge), where the total work over a closed path is always zero.

  • In this case, the path is also a closed loop, and the area of the loop does not affect the work done by the electric field. The test charge moves around the loop, but since the electric field from a point charge is conservative, the total work done over this closed loop is zero.

Here we can observe that the work done in both of the cases is zero. The work done due to the electric force on the charge is in the closed-loop and the value of it is equal to zero.

 

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