Final answer:
The potential difference VC - VA is -50 V, calculated by dividing the net work done in moving a charge from C to A by the charge.
Step-by-step explanation:
The question asks for the potential difference VC - VA given the work done to move a charge between two points. The potential difference, in volts (V), is calculated by dividing the change in potential energy by the charge. According to the formula (VB - VA) = ΔPE / q, where ΔPE is the change in potential energy and q is the charge
Work done from A to B is +4.0 μJ and from C to B is -5.0 μJ. For a positive charge, moving from a higher potential to a lower potential gives positive work, thus B is at a higher potential than A. To find VC - VA, we combine the work done from A to B and C to B. If moving from C to B requires negative work, C is at a lower potential than B. The net work done in moving from C to A is the sum of the work from C to B and A to B: -5.0 μJ + 4.0 μJ = -1.0 μJ, which is equivalent to the change in potential energy when moving from C to A.
Now, we can find VC - VA by dividing this net work by the charge: VC - VA = (-1.0 μJ) / (20 nC). Converting μJ to joules (1 μJ = 10^-6 J) and nC to coulombs (1 nC = 10^-9 C), we get
VC - VA = (-1.0 × 10^-6 J) / (20 × 10^-9 C) = -50 V.