I was reading my physics textbook and came across this sentence:
When a charge moves in an electric field, unless its displacement is always perpendicular to the field, the electric force does work on the charge.
So it is saying that if the displacement is perpendicular to the field, the electric force does no work on the charge.
- Why is it so?
- By perpendicular to the field does it mean perpendicular to certain field line?
- Is it implying that if the displacement is perpendicular to certain field line, some other force does work on it (but not the electric force)?
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But how to be "perpendicular to certain field line" when field lines are normally curved?
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Let's say it means literally the field but not field lines, then how to be "perpendicular to the field" when the field is not even a straight line but a 3 dimensional region in which electric force is effective regardless of the presence or absence of a material medium?
Best Answer
This is just a special case of $dW = \vec{F} \cdot d\vec{r}$ for $\vec{F} = q\vec{E}$. The statement is saying that if $\vec{E}$ is perpendicular to $d\vec{r}$ then $q\vec{E}=\vec{F}$ will also be perpendicular to $d\vec{r}$, and so $dW$ will be zero.
It means perpendicular to the field at the location of the charge being acted on.
No.
and 5. Imagine a point charge orbiting a second point charge in a circular orbit (for example, a classical picture of an electron in a circular orbit around a hydrogen nucleus). Similar to the case of a circular planetary orbit, no work is done because the direction of motion is perpendicular to the field lines.