1. Nov 7, 2004

### agirlsrepublic

k im really confused about how to go about setting up the intergral of Eds. how do u choose the limits of integration and how do u know whether to write Va-Vb= -(integral) E ds
or Vb-Va = - (integral) E ds

its really frustrating me
i thought i understood but i realised i really dont
my teacher said something about choosing the direction of ds to be the same as the e field..but that doesnt help me much
im just confused

itd be really cool if someone could straighten this out
thanks

Last edited: Nov 7, 2004
2. Nov 7, 2004

### Tide

First, realize that

$$\vec E = - \nabla V$$

(note the minus sign) and

$$\int_a^b \nabla V \cdot d\vec s = -\int_a^b \vec E \cdot d\vec s$$

or

$$V(b) - V(a) = -\int_a^b \vec E \cdot d \vec s$$

so your E ds is really $\vec E \cdot d \vec s$