Lenz's Law Physics Problem

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.

A metal rod is moved to the right through a magnetic field. A charge separation is induced as shown below. Determine the direction of the magnetic field.

A current carrying loop has a radius of 3 cm. The current is 7 A in the counter clockwise direction. Find the magnetic dipole moment, $\vec{\mu}$