1. Loop moving into a Constant Magnetic Field. Consider a square loop with side length 1m moving at a rate 0.1 m/s in the +x-direction into a magnetic field 6m long with constant strength and direction of B = 1 T ?̂ (into the page). At what angle should the normal of the loop’s area be to the background magnetic field in order to maximize the magnetic flux through the loop?

1.  A DC power line for a light-rail system carries 950 A at an angle of 33° to the Earth’s 5.00 × 10-5 T magnetic field. What is the magnitude of the force (in N) on a 125 m section of this line?  2. Consider a 150 turn square loop of wire 15.5 cm on a side that carries a 56 A current in a 1.6 T field. What is the maximum torque on the loop of wire in N⋅m?  What is the magnitude of the torque in N⋅m when the angle between the field and the normal to the plane of the loop θ is 14°?  3.  Consider two two long, straight, parallel, current-carrying wires, separated by a distance d = 4.5 cm, as shown in the figure. The left wire is directed out of the page with current I1, and the right wire is directed into the page with current I2. The point P is a distance d from both wires, so the wires and the point form an equilateral triangle. If both wires are carrying a current of 3.5 A, what is the magnitude of the magnetic field, in teslas, at point P?  If the current from the left wire is 3.5 A…

002 A wire in which there is a current of 3.7 A is to be formed into a circular loop of one turn. If the required value of the magnetic field at the center of the loop is 9.56 T, what is the required radius? The permeability of free space is 1.25664 x 10-6 T-m/A. Answer in units of cm.

3. Current head-on to point P: Consider the case where the current is heading straight toward the point where we want the magnetic field. What is the magnetic field at the point P shown? Hint: consider a small piece ds and think about what the Biot-Savart law tells you. Holds x f 4πr2 Think about the angle between ds and î. dB 7 D P