Magnetic Dipoles

The leading term in the vector potential multipole expansion involves:

$\oint d\mathbf{l}'$

What is the magnitude of this integral?

1. $R$
2. $2\pi R$
3. 0
4. Something entirely different/it depends!

The vector potential for the dipole is:

$\mathbf{A}_d = \dfrac{\mu_0}{4\pi r^2} \mathbf{m} \times \hat{\mathbf{r}}$

What is the magnitude of that cross product $|\mathbf{m} \times \hat{\mathbf{r}}|$?

1. 1
2. $m$
3. $m r\sin\theta$
4. $m\sin\theta$
5. Something else?

The vector potential for the dipole is:

$\mathbf{A}_d = \dfrac{\mu_0}{4\pi r^2} \mathbf{m} \times \hat{\mathbf{r}}$

If the magnetic dipole moment points in the $\hat{\mathbf{z}}$ direction, what is the direction of the $\mathbf{A}_d$?

1. $\hat{\mathbf{z}}$
2. $\hat{\mathbf{\phi}}$
3. $\hat{\mathbf{r}}$
4. $\hat{\mathbf{m}}$
5. Something else?

Two magnetic dipoles $m_1$ and $m_2$ (equal in magnitude) are oriented in three different ways.

Which ones can produce a dipole field at large distances?

1. None of these
2. All three
3. 1 only
4. 1 and 2 only
5. 1 and 3 only

Two magnetic dipoles $m_1$ and $m_2$ (unequal in magnitude) are oriented in three different ways.

Which ones can produce a dipole field at large distances?

1. None of these
2. All three
3. 1 only
4. 1 and 2 only
5. 1 and 3 only

Magnets, how do they work?

Insane Clown Posse - Miracles

Paramagnetism & Magnetic Domains