Work Done in Moving a Point Charge Around a Circular Arc

The amount of work done in moving a point charge Q around a circular arc of radius 'r' at the center of which another point charge 'q' is located can be determined using the following steps:

Step 1: Determine the Electric Potential Energy of the System

The first step is to determine the electric potential energy of the system. This can be done using the formula:

U = kQq/r

where U is the electric potential energy, k is Coulomb's constant, Q is the charge of the point charge being moved, q is the charge of the point charge at the center of the circular arc, and r is the radius of the circular arc.

Step 2: Determine the Change in Electric Potential Energy

The next step is to determine the change in electric potential energy as the point charge Q is moved around the circular arc. This can be done using the formula:

ΔU = Uf - Ui

where ΔU is the change in electric potential energy, Uf is the final electric potential energy of the system when the point charge Q has completed its circular motion, and Ui is the initial electric potential energy of the system.

Step 3: Determine the Work Done

The final step is to determine the work done in moving the point charge Q around the circular arc. This can be done using the formula:

W = -ΔU

where W is the work done and ΔU is the change in electric potential energy. The negative sign indicates that the work done is negative, which means that the point charge Q loses energy as it moves around the circular arc.

Therefore, the amount of work done in moving a point charge Q around a circular arc of radius 'r' at the center of which another point charge 'q' is located is equal to the negative change in electric potential energy of the system.