A test charge + q moves five times along a circular path of radius r with the charge of + Q at the center. The work done is
Work done as we know is defined as a product of force implied and the displacement occurred
W= F.s
Similarly, in an electric field, the path taken really doesn't make a difference, it's basically the difference in the potentials between those two points.
W= Q. [V(a) - V(b)]
Where W = work done
Q = charge against which the particle is moved
V(a) or V(b) = Electric potential at those two points
Now, since the electric potential is same at all points on the circle with respect to the charge at the centre of the circle, no matter how many rounds the charge +q take, the work done will be ZERO.
Hello!
As the test charge is moved along a circular path with another charge in the middle, the charges are separated by the same distance throught the movement. Hence there is no displacement. Also, the force acting and displacement will always be perpendicular when a charge is moving in a circular path. Hence the angle between these quantities will be 90 and cos(90)=0. Hence the work done will be Zero always.
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