Assignment:
Part 1
• Determine the force on a semicircular wire with current I in the presence of a field B.
• An electron with a speed of 3.8 105 m/s enters a uniform magnetic field of magnitude 0.053 T at an angle of 35° to the magnetic field lines. The electron will follow a helical path.
(a) Determine the radius of the helical path.
(b) How far forward (parallel to the magnetic field lines) will the electron have moved after completing one circle?
• A conducting rod of length L slides freely down an inclined plane, as shown in the figure. The plane is inclined at an angle θ from the horizontal. A uniform magnetic field of strength B acts in the positive y-direction. Determine the magnitude and the direction of the current that would have to be passed through the rod to hold it in position on the inclined plane.
• A copper wire with density ρ = 8960 kg/m3 is formed into a circular loop of radius 47.0 cm. The cross-sectional area of the wire is 1.00 10-5 m2, and a potential difference of 0.020 V is applied to the wire. What is the maximum angular acceleration of the loop when it is placed in a magnetic field of magnitude 0.20 T? The loop rotates about an axis through a diameter.
• A semicircular loop of wire of radius R is in the xy-plane, centered about the origin. The wire carries a current, i, counterclockwise around the semicircle, from x = -R to x = +R on the x-axis. A magnetic field, B , is pointing out of the plane, in the positive z-direction. Calculate the net force on the semicircular loop.
Part 2
• Suppose that the magnetic field of the Earth were due to a single current moving in a circle of radius 2960 km through the Earth's molten core. The strength of the Earth's magnetic field on the surface near a magnetic pole is about 6. 10-5 T. About how large a current would be required to produce such a field?
• A square loop, with sides of length L, carries current i. Find the magnitude of the magnetic field from the loop at the center of the loop, as a function of i and L.
• The figure below shows a Helmholtz coil used to generate uniform magnetic fields. Suppose the Helmholtz coil consists of two sets of coaxial wire loops with 13 turns of radius R = 71.0 cm, which are separated by R, and each coil carries a current of 0.134 A flowing in the same direction. Calculate the magnitude and the direction of magnetic field in the center between the coils.
• What is the magnitude of the magnetic field inside a long, straight tungsten wire of circular cross section with diameter 3.6 mm and carrying a current of 2.7 A, at a distance of 0.5 mm from its central axis?