# Quick Question about Electric Fields

Electric field lines always point toward:

(_) positive charge
(_) a region of higher potential
(_) ground
(_) a region of lower potential
(X) none of these

Now, i thought that electric fields point towards the negative charge. I submitted my homework, and i missed it. I was just wondering if anyone could explain to me why electric field lines dont point toward a negative charge. Everything i read lead me to that conclusion, so i put "none of these" and missed it. Is the correct answer "a region of lower potential"

I'd just like to know cause i thought i did, but apparantly didnt.

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berkeman
Mentor
Hmmm. That's a tricky one. I think the most accurate answer would have been that electric field lines always originate on + charges and terminate on - charges, like the lines of an electric dipole. And if you think about the dipole and it's E-field fountains, yeah it's true that the E-field doesn't point directly at a charge for a lot of its shape. So I'd be inclined to say that answer (d) above seems pretty close, since E=-grad[V]. Was (d) the correct answer?

I believe that's how many undergrad textbooks (somewhat sloppily) put it: $$\vec{E}\left(\vec{r}\right)=-\vec{\nabla}V\left(\vec{r}\right)$$ implies that the field lines go from a region of lower potential to a region of higher potential.

berkeman
Mentor
No, the negative sign means that the E field is pointing down the gradient of the potential V, toward a lower potential. Think about what a positive charge does in the presence of an electric field -- it accelerates in the direction of the E field. That means it gains KE and loses PE. Just like a mass accelerates in the direction of the gravitational field, and gains KE and loses PE.

berkeman said:
No, the negative sign means that the E field is pointing down the gradient of the potential V, toward a lower potential.
Big whoops. Thanks. I wrote the opposite of what I meant :/

Gravitation is a good analogy, I like that.

To the OP:
You probably remember from classical mechanics that for conservative forces, $$\vec{F} = -\vec{\nabla}V$$. A way to think about this is that things subject to this force "want" to get into a state with the lowest possible potential (think of dropping a ball).

Doc Al
Mentor
jakeowens said:
Now, i thought that electric fields point towards the negative charge. I submitted my homework, and i missed it. I was just wondering if anyone could explain to me why electric field lines dont point toward a negative charge. Everything i read lead me to that conclusion, so i put "none of these" and missed it.
If you just had a single negatively-charged point charge, then the field everywhere would point towards the negative charge. But, when there are other charges around, things get more complicated. (For example, what if there were two negative charges? The field everywhere can't point towards both if the charges are separate.)

Note that they wisely did not list "negative charge" as an option.
Is the correct answer "a region of lower potential"
Yes. As others have pointed out, this is always true and is the right answer.