An electric force moves a charge of +1.65 multiplied by 10-4 C from point A to point B and performs 6.40 multiplied by 10-3 J of work on the charge.

(a) What is the difference (EPEA - EPEB) between the electric potential energies of the charge at the two points?
(b) Determine the potential difference (VA - VB) between the two points.
(c) State which point is at the higher potential.

(a) Work done by the field is MINUS the change of potential energy.

So the EPE change is -6.40*10^-3 J
Since they are asking for EPEA - EPAB, that is +6.40*10^-3 J.

(b) Divide the previous answer by the charge, 1.64*10^-4 C

(c) Point A has higher potential, since work was done on a positive charge going from A to B

To answer these questions, we need to use the formula for electric potential energy and the formula for potential difference:

(a) The difference in electric potential energies (EPEA - EPEB) is equal to the work done on the charge (W):

EPEA - EPEB = W

Plugging in the values:
EPEA - EPEB = 6.40 x 10^(-3) J

(b) The potential difference (VA - VB) is given by the equation:

VA - VB = EPEA - EPEB / q

Where q is the charge. Since in this case, the charge is positive (q = +1.65 x 10^(-4) C), we can use the formula:

VA - VB = EPEA - EPEB / q

Plugging in the values:
VA - VB = (6.40 x 10^(-3) J) / (1.65 x 10^(-4) C)

(c) To determine which point is at the higher potential, we compare the potential values. If VA > VB, then point A is at a higher potential than point B.

Now, let's calculate the answers:

(a) The difference in electric potential energies is 6.40 x 10^(-3) J.
(b) The potential difference is (6.40 x 10^(-3) J) / (1.65 x 10^(-4) C).
(c) Compare the potential values (VA and VB) to determine which point is at the higher potential.