Conceptual Issue RE: electric potential difference

[keroberous]

Homework Statement

My main conceptual issue here surrounds positives and negatives as they apply to electric potential difference. I will post two questions that illustrate my confusion, if that's ok.

1) The electrons in an old TV picture tube are accelerated through a potential difference of 2.5 × 10⁴ V. Calculate the change in the electric potential energy of the field.

2) Calculate the magnitude of the electric field if an electron moves a distance of 15 cm through a potential difference of 1.5 × 10⁴ V.

Homework Equations

$\Delta E_E = q \Delta V$

$\varepsilon= - \frac {\Delta V} {\Delta d}$

The Attempt at a Solution

As I mentioned, my issues revolve around the signs and how to interpret the results. For example, for the first question we get that:

$\Delta E_E = q \Delta V \\ \Delta E_E =(-1.6 \times 10^{-19})(2.5 \times 10^4) \\ \Delta E_E = -4.0 \times 10^{-15}$

This is all well and good considering we were told the electrons were accelerating so we expect them to lose potential energy (and presumable gain kinetic energy). But if we consider a proton (for instance) in the same field, then $\Delta E_E = 4.0 \times 10^{-15}$ Again this makes sense if the protons are going in the same direction the electrons were. But how would we know that if we weren't originally told the electrons are accelerating? All of the values for potential difference given in the text I'm using are positive. Obviously potential difference should be able to be negative according to its definition, i.e. if $V_f < V_i$.

For the second question we get that:

$\varepsilon= - \frac {\Delta V} {\Delta d}\\ \varepsilon= - \frac {1.5 \times 10^4} {0.15}\\ \varepsilon= -1.0 \times 10^5$

I know the question only asks for the magnitude of the electric field, but using the equation as given does produce a negative. The text offers this explanation of the negative: "The negative sign indicates that the field extends from high to low potential." But doesn't the electric field always point in that direction?

Thanks for your help!

 

[Doc Al]

Again this makes sense if the protons are going in the same direction the electrons were. But how would we know that if we weren't originally told the electrons are accelerating?

Presumably, you are given the potential difference from point A to point B, which is the path the particles travel. If the potential difference is positive, as given here, you know the direction of the field (from B to A) and that electrons will speed up and protons slow down.

The text offers this explanation of the negative: "The negative sign indicates that the field extends from high to low potential." But doesn't the electric field always point in that direction?

Sure. The bit about electrons is just to trick you. And they are just explaining the meaning of the minus sign (which you already know).