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.

shouldnt it be that B and C are along equipotential lione so their potential difference is zero?

You are correct. According to the information provided, points B and C are both on equipotential lines, meaning they have the same electric potential. Therefore, the potential difference between points B and C, as well as the potential difference between points A and B, will be zero.

To understand this concept further, let's break it down step by step:

(a) To find the potential difference between points B and A (VB - VA), we can use the equation:

∆V = VB - VA = W / q

Where ∆V is the potential difference, W is the work done by the electric field (given as 3.66 x 10^-19 J), and q is the charge of the electron.

Since the question does not provide the charge of the electron explicitly, we can utilize the known value of the elementary charge (e) which is 1.6 x 10^-19 C. So, the potential difference between points B and A can be calculated as:

∆V = (3.66 x 10^-19 J) / (1.6 x 10^-19 C) = 2.29 V

(b) As points B and C are on equipotential lines, their potential difference (VC - VA) will be zero.

(c) Similarly, since points B and C share the same electric potential, the potential difference between them (VC - VB) will also be zero.

Therefore, the answers are:
(a) VB - VA = 2.29 V
(b) VC - VA = 0 V
(c) VC - VB = 0 V