What is the difference between electric field and electric force? Both seem to do the same thing, but their formulas are different.
$\begingroup$
$\endgroup$
Add a comment
|
3 Answers
$\begingroup$
$\endgroup$
The electric field is a function on spacetime, $\vec E:\mathbb{R}^4\to\mathbb{R}^3$, that can be used to calculate the electric force experienced by a charge at a given point. This is given by the equation $$\vec F = q\vec E(\vec x,t)$$ where $\vec F$ is the electric force on the charge $q$, located at position $\vec x$ at time $t$. The key difference between these two quantities is that electric field is a function of position (and time), whereas the electric force applied by an electric field is associated with a particular object.
$\begingroup$
$\endgroup$
Field is force per unit charge. The field tells you what the force would be on a particle with a charge of 1, if such a particle was there. Force is what the actual force is on whatever particle is there. The force that a particle puts on another particle of charge of 1, is the same as the field that first particle makes.
But if the second particle has a charge of 100, the first particle’s field will be 1/100th as much as the force it is putting on the second particle. Because the first particle’s field means how much force it’d put on a particle of charge 1, if it was there. (Regardless of what is there).
$\begingroup$
$\endgroup$
In essence, an electric field $E$ is electric force $F$ per charge $q$:
$$E=\frac Fq.$$
We associate any point with an electric field. This is thus the force that would be applied to a unit charge, should it be placed there. So,
- the electric field represents what will happen and it is always present, where as
- the electric force (any force) represents what is happening and is only present where there is something that the force is acting on.
