Questions/Comments on Electricity and Magnetism

Thu, Feb 6, 10:48 p.m. - Hey, I am confuse with the magnetic field and magnetic moment, could you tell me what's the different between them?

First, sorry about the delay in answering. I somehow missed this question.

The magnetic field is maybe the easier one to understand. Like the electric field, it is a source of force. A charge $q$ in an electric field $\vec E$ feels an electric force $\vec F_e = q\vec E$. A charge $q$ moving with velocity $\vec v$ in a magnetic field $\vec B$ feels a magnetic force $\vec F_m = q\vec v\times \vec B$.

That doesn't explain where magnetic fields come from, but it explains what they do: magnetic fields create forces on moving charges.

A magnetic moment is just a property of a current loop. A current loop has a current $I$ and it has some area vector $\vec A$ whose magnitude is equal to the area of the loop and whose direction is perpendicular to the plane of the loop. And it might have $N$ turns, or it might have just one turn (so $N=1$). We take these quantities and multiply them together to define the magnetic moment

$\vec\mu = N I \vec A$

And we do that because it is useful for telling us the torque on that current loop if it located in a magnetic field: $\vec\tau = \vec\mu\times\vec B$.

So that's what the magnetic moment does: it's a property of a current loop that helps us find the torque on the current loop.

Tue, Jan 28, 11:01 p.m. - Hey, I was wondering when do we need to put arrows on top of E (electric field) and F (electric force)? When do we not need to put arrows? Thanks!

This is a question about vectors in general. Forces and the electric field are vectors, so they need to be written with the arrow, i.e. $\vec F$ or $\vec E$.

But remember that vectors have both magnitude and direction, and sometimes we specifically mean the magnitude of the vector. One example is with electric flux in a uniform electric field, which is given by

$\Phi_E = \vec E \cdot \vec A = E A \cos\theta$

The first $\vec E$ has the arrow because electric flux is given by the dot product of the electric field (which is a vector) with the area vector. But in the second expression we have $E$ without the arrow. This is because the dot product of two vectors equals

(magnitude of the first vector) x (magnitude of the second vector) x (cosine of the angle between them)

We really mean the magnitude of the electric field in the second expression, so we write $E$ without the vector.