Which equation should be used to calculate electric potential?

[henry3369]

Homework Statement

So I've read two difference textbooks for electric potential and both of them define them in a different way and I'm confused as to which method I use because they yield results with different signs.

The two ways I've seen it are:
1. ΔV = Vb - Va = -Ed

2. Va-Vb = Ed

Do both of these mean the same thing? I was doing a few problems today using equation 1, and I kept getting the correct magnitude, but wrong sign (usually solved and got negative, but it was positive).

Homework Equations

ΔV = Vb - Va = -Ed
Va-Vb = Ed

The Attempt at a Solution

 

[SammyS]

Homework Statement

So I've read two difference textbooks for electric potential and both of them define them in a different way and I'm confused as to which method I use because they yield results with different signs.

The two ways I've seen it are:
1. ΔV = Vb - Va = -Ed

2. Va-Vb = Ed

Do both of these mean the same thing? I was doing a few problems today using equation 1, and I kept getting the correct magnitude, but wrong sign (usually solved and got negative, but it was positive).

Homework Equations

ΔV = Vb - Va = -Ed
Va-Vb = Ed

The Attempt at a Solution

They are the same.

What is $\displaystyle\ -(V_b-V_a) \$ ?

 

[ScifiGen]

Since potential is measured in terms of work done per unit charge, if a charge is moved between two points against the field, then work done is positive and naturally , potential is greater at the second point, so the difference in potential is : (Potential at 2nd point)-(Potential at first point).Thus this potential is positive.However, as mentioned, this work shall be done against the field, so if you are equating change in potential to field, the negative sign is compulsory.
Thus, Difference in potential is necessarily Vb-Va, if b is the second point.
If you are equating this to El. field, then the above difference in potential is equated to -Ed (Notice the negative sign applied here...)