Solenoid Magnetic Field

A region of the rectangular wire loop shown below sits in a uniform magnetic field directed into the page, $\vec{B}$ = 7.0 T. The coil is being pulled to the right (shown in blue) at a velocity of 3 m/s. Note that the loop is being pulled into a region that does not contain a magnetic field. Find the:

C. Force required to pull the wire loop at constant velocity

A magnetic field increases with time as described by the function, B(t) = 4 + 6t. Given a coil with 880 turns, N = 880, and an area A = (.05m)$^2$, find the induced voltage in the coil.

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.