When an electron moves from A to B along an electric field line in Fig. 24-29, the electric field does 3.66 x 10-19 J of work on it. What are the electric potential differences (a)VB - VA, (b)VC - VA, and (c)VC - VB?

in the picture there r four field lines going from down to up that is from B to A. C is on otheer field line along the curve joining B with C. they r in eqvipotential

The potential energy difference EB - EA equals the charge (-e) times the voltage difference. Thus

3.66*10^-19 J = (-1.60*10^-19 C)(VB - VA)
VB - VA = 2.3 Volts

B and C are along what is called an equipotential line, not a field line.
Field lines are everywhere perpendicular to equipotential lines.
Therefore VC - VA = 0

Since VC = CA, VC - VB = VA - VB
= -2.3 V

drwls, that didn't work for my problem.

To find the electric potential differences VB - VA, VC - VA, and VC - VB, we need to understand the relationship between work done and electric potential.

The work done on a charge moving through an electric field is given by the equation:

W = qΔV

Where W is the work done, q is the charge, and ΔV is the potential difference between two points.

In this case, the work done is given as 3.66 x 10^-19 J, and we need to find the potential differences.

(a) VB - VA:
Here, we know the work done and we need to find the potential difference between points B and A.

W = qΔV
3.66 x 10^-19 J = q(VB - VA)

Since points B and A are in the same electric field line, they are at the same electric potential (equi-potential), so the potential difference between them is zero.

Therefore, VB - VA = 0.

(b) VC - VA:
Now, we need to find the potential difference between points C and A.

W = qΔV
3.66 x 10^-19 J = q(VC - VA)

Since points C and A are on different electric field lines, they have different electric potentials.

Therefore, VC - VA ≠ 0.

(c) VC - VB:
Finally, we need to find the potential difference between points C and B.

W = qΔV
3.66 x 10^-19 J = q(VC - VB)

Since points C and B are on different electric field lines, they have different electric potentials.

Therefore, VC - VB ≠ 0.

To calculate the exact values of VC - VA and VC - VB, you would need to know the charges of the particles and the distance between the points.