# 2 tough questions

1. Oct 28, 2005

### don23

I need help with these two questions:
1. A particle of mass 'm' and charge '-q' moves in a circular radius 'R' about a fixed charge 'Q.' The angular frequency for the orbit is given by
w0^2=q*Q/(4*pi*e0*m*R^3).
A uniform magnetic field of magnitude B is in the direction perpendicular to the plane of the orbit is turned on. As a result, the angular frequency is changed to w0+dw. Assuming that B is sufficiently small so that product of B and dw can be neglected, calculate dw.

2. An electric motor consists of a current-carrying wire loop in a constant magnetic field B. The field produces a torque that tends to rotate the loop so that the loop's magnetic dipole, u and B become aligned. When that happens, a split-ring commutator reverses the current direction, so that u changes its orientation by 180 degrees, and the torque acts to continue the rotation. Suppose that u and B start out almost antiparallel. Plot the magnitude of torque as a function of the angle between u and B, as this angle runs from -pi to 0. At 0 degrees, the commutator reverses the current. Plot the torque through another half turn. What is the average value of the torque through a full turn if the current in the motor is 6.2 A, the magnitude of B is 0.45 T, and the area of the loop is 54 cm^2?

Ok...for the plotting of the magnitude of the torque, I think it would be much like that of a sine graph, with the -180 and 0 and 180 all at zero and at -45 and 45 degrees at a maximum value. I am not sure how to find the average torque, but I know that the torque value is between 0, when anitparallel and parallel, and 0.0015 N/m. How would I find the average?