## PHYS208 Fundamentals of Physics II

### Hint for Ch. 29, 54E There will be a force on b pointing out of the page (screen), one on a pointing into the page (screen), and no force acting on c from the magnetic field. Don't forget the sine of the angle between iL and B in evaluating the magnitude of the magnetic force.

These two forces are equal and oppositely directed, acting through different lines of action, the center of each section. They form a force couple tending to rotate the loop about an axis midway between these two lines of action.

### Hint for Ch. 29, 56E

Use the formula for the dipole moment of a current loop, NiA; the relationship for multiple turns N is that the radius of the loop will be L = (2 pi rN. Substitute this into pi r2 for the area and maximize.

### Hint for Ch. 29, 61P

This is not really a "torque on a dipole" question, but rather a simple circuit problem.

a) What resistor needs to be added in series with the galvanometer to "drop" all but 0.122 V of the applied 1.00 V.

b) What resistor needs to be added in parallel to the galvanometer to shunt all but 1.62 mA of the 50.0 mA.

### Hint for Ch. 29, 62P

It is easiest to consider the loops of wire to form a dipole. The torque created will be out of the page (screen) tending to rotate the spool up the incline.

The additional forces acting on the spool are the force of gravity mg, acting downward from the center of mass, the normal force of the incline N, acting perpendicularly to the incline through the center of mass, and the force of friction Ffric, acting up the incline at the point of contact.

Draw a free body diagram!

Set up Newton's second law for acceleration down the incline and Newton's second law for rotation about the center of the spool. Find the least current (least dipole moment) that will be required for both the linear acceleration and the angular acceleration to be zero.

"http://www.physics.udel.edu/~watson/phys208/exercises/hints/0327.html"
Last updated March 26, 1998.
Copyright George Watson, Univ. of Delaware, 1997.