Question

In the situation of Question 7, is the work done by your force positive, negative, or zero if the particle is moved (a) from Ato B, (b) from Ato C, and (c) from Bto D? (d) Rank those moves according to the magnitude of the work done by your force, greatest first.

Short answer

Answer:

1. The work done by our force is the particle is moved from A to B is positive.
2. The work done by our force is the particle is moved from A to C is positive.
3. The work done by our force is the particle is moved from B to D is negative.
4. The rank of the moves according to the magnitude of the work done by our force is .

Step-by-step solution

The given data

Figure 24-30 gives a system of three-charged particles.

Understanding the concept of electric potential and work done

Considering the relation between the potential and work done, the required change in work done due to the action of moving a charge can be calculated. Again, the electric potential at each point is considered to get the net work done, which is the difference between the two potentials multiplied by the amount of charge being moved.

Formulae:

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

The work done by a charge,W=Vq (ii)

a) Calculation of the work done by force if particle is moved from A to B

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:

Hence, the value of work done is positive.

b) Calculation of the work done by force if particle is moved from A to C

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

Hence, the value of work done is positive.

c) Calculation of the work done by force if particle is moved from A to C

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

Hence, the value of work done is negative.

d) Calculation of the rank of the moves according to the work done

From the above calculated values, it can be seen that the rank of work done can be given as:

Hence, the required rank value of the moves is .