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 line so their potential difference is zero?

I answered this yesterday. Yes. B and C are along an equipotential line, not a field line

yes u answered it yesterday bt i got Vc-Va and Vc-Vb wrong so i wanted to clear my doubt that Vb-Va should be zero?

VB - VA is not zero. Work is done on the electron moving from A to B. Since its charge is negative, the voltage is higher at B. I may have gotten the signs wrong in my previous answer.

You make a statement that B and C ar equipotential, so the voltages there are the same

parts a and b should be the same since its the same radial distance from equipotential line that A is on, right?

In the given scenario, you are correct that points B and C are on the same equipotential line and therefore have the same electric potential. The electric potential at a point in an electric field is defined as the amount of work done per unit charge to bring a positive test charge from infinity (or a reference point with zero potential) to that point.

To determine the electric potential differences mentioned, let's use the formula:

Electric potential difference (ΔV) = Work done (W) / Charge (q)

(a) VB - VA:
Given that the electric field does 3.66 x 10-19 J of work, it implies that the work done (W) is 3.66 x 10-19 J. Since the electric potential difference is the work done per unit charge, we need the value of the charge (q) to determine ΔV.

(b) VC - VA and (c) VC - VB:
As points C and B lie on the same equipotential line, their electric potentials are the same. Therefore, the electric potential difference between VC and VB is zero. Additionally, since points C and A are also on the same equipotential line, their electric potential difference (VC - VA) is also zero.

So, to summarize:
(a) VB - VA: Requires the charge (q) value to compute.
(b) VC - VA: The difference is zero as they are on the same equipotential line.
(c) VC - VB: The difference is zero as they are on the same equipotential line.

Remember that equipotential lines are perpendicular to the electric field lines and represent points with the same electric potential.