### Pset 9, Abubakar Abid (It may take a second for the LaTeX-javascript library to load...)

1. Diamagnetism can be estimated as
$$ \chi_m = \frac{M}{H} = -\mu_0 \frac{q^2 Z r^2}{4 m_e V} $$
Using numbers from literature, and assuming that the solid is (predominantly) carbon, we find that susceptibility is:
$$ \chi_m = -\mu_0 \frac{q^2 6 (70 \text{pm})^2}{4 m_e 4/3 \pi (70 \text{pm})^3} $$
$$ \chi_m = 0.0001812$$
The force is
$$ F = V \mu_0 \chi_m H \frac{dH}{dz} = mg$$
For a magnetic field gradient that goes to zero over the frog
$$ F = V \mu_0 \chi_m \frac{H^2}{\Delta z} = mg$$
$$ H^2 = \frac{\Delta z \rho g}{\mu_0 \chi_m}$$
Assuming \(\Delta z\) is 5 cm, then
$$H = 1.467 MA/m$$
This would correspond to a magnetic field strength of approximately
$$ B = \mu_0 H = 1.8 T$$
2. The field strength of a magnetic dipole is

6. The coercivity of this material is roughly 300 Oersted, which corresponds to 0.03 Teslas. The magnetic field from a current source is
$$B = \mu_0 I / (2\pi r)$$
$$0.03 T = \mu I / (2\pi 1 cm)$$
$$I = 1500 A$$