91Ó°ÊÓ

1. Figure 24-30 gives a system of three-charged particles.
2. Particle of charge is moved from point A to point D.

The net potential energy for bringing a charge from one point to another is given by the total energy due to all the charges present in the system. Thus, for two positive charges, net potential energy is positive. Now, for work done, we consider the polarity of charges only. For equal polarity the, work done is found to be positive apart from its value. The work done by our force depends on the path followed by our force. Thus, for the opposite path and force direction, the work done will be negative.

Formulae:

The potential energy at a point due to point charge,V=kq\r (i)

The work done by a charge,$W=Vqor{∫}_{}^{}{F}_{ext}dr$ (ii)

The electric potential energy due to an external work done, (iii)

Potential at point A is given using the given data in equation (i) as follows:

Now, the potential at point B is given using the data in equation (ii) as follows:

Now, the potential at point C is given using the data in equation (ii) as follows:

Now, the potential at point D is given using the data in equation (ii) as follows:

Thus, the work done in bringing the charge +q from point A to B can be given using the above values in equation (ii) as follows:

Now, the change in electric potential energy of the system can be given using equation (iii) as follows:

Hence, the potential energy change is zero.

From the given data, it can be seen that all the charges involve in the process are positive in nature. Thus, the nature of external force would be repulsive $(F_{ext}=-ve).$Hence, the work done by the external force considering equation (ii) is negative.

From calculations of part (a), it can be seen that the value of work done is found to be

Hence, the value of work done is zero.

Now, the work done in bringing the charge +q from point B to C can be given using the above values in equation (ii) as follows:

Now, the change in electric potential energy of the system can be given using equation (iii) as follows:

From the given data, it can be seen that all the charges involve in the process are positive in nature. Thus, the nature of external force would be repulsive $(F_{ext}=-ve).$Hence, the electric potential energy, work done by electric force and our force will be zero, negative and zero respectively.