1.1 Derive Biot-Savart's Law for the magnetic field at a point due to the current in a small segment of a wire.
Note: remember the substitution used in the solution. This is one of the more common problem-solving strategies in magentostatics.
1.2 Find the magnetic field function by an infinite straight wire, finite straight wire, finite solenoid, infinite solenoid, and a toroid.
1.3 Consider an infinitely long, cylindrical conductor of radius R carrying a current I with a non-uniform current density \(J\ =\ \alpha r\), where \(\alpha\) is a constant. Find the magnetic field everywhere.
1.4 If a current passes through a spring, does the spring stretch or compress?
1.5 A circular disk of radius R with uniform charge density σ rotates with an angular speed ω. Show that the magnetic field at the center of the disk is \(B\ =\ \frac{1}{2}\mu_0\sigma\omega R\).