Magnetic Dipole Moment

As a steel guitar string vibrates, the component of the magnetic field perpendicular to the area of a pickup coil nearby is given by B(t) = 50 mT + (3.20 mT) Sin (1046$\cdot\pi$t). The circular pickup coil has 30 turns, a radius of 2.70 mm, and a resistance of 0.10 $\Omega$. What is the magnitude of the maximum current induced in the coil?

A square coil, with dimensions l = 12.0 cm, w = 7.0 cm, is placed d = 3.0 cm above a wire that carries a current of 30.0 A. Find the magnetic flux through the wire.

The wire depicted below has a current I = 25.0 A, r$_1$ = 9.0 cm and r$_2$ = 6.0 cm. Find the magnetic dipole moment $\vec{\mu}$.

The circuit below is a square with sides L and is placed in a magnetic field directed into the screen. Attached to the circuit are two light bulbs of resistance R $\Omega$. The magnetic field is described by the function B(t) = at + b. What is the current in the circuit and in what direction does it flow. Also how much power is dissipated in light bulb 1.