#$&*
Phy 242
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Test 3 Question
** **
A proton, mass 1.7 * 10^-27 kg, moves at 9.3 * 10^6 m/s to the East in a uniform vertical magnetic field. If the path of the electron is a circle of radius 5.7 cm, what is the strength of the field? If the proton circles in the clockwise direction as viewed from above, is the field upward or downward?
** **
I'm starting to study for test 3. Where it says If the path of the electron is a circle of radius 5.7 cm, what is the strength of the field?, did you really mean to say if the path of the PROTON... if that's not what you meant, could you please explain how to set this problem up? Thank you
** **
How do I do this problem?
@&
The randomizer got the wrong word.
It should have been electron, the first particle mentioned, not proton.
*@
#$&*
Phy 242
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
More Test 3 Questions
** **
A thin circular conducting disk carries total current I. The current path is at every distance from the center of the disk circular, and the center of each circle is the center of the disk. Find the magnetic field at the center of the disk, provided the current density is constant (i.e., the current is uniformly distributed throughout the disk).
@&
Do study the book's development of the integrals for electric and magnetic fields for various shapes.
Current density is the amount of current per centimeter as measured along a radial line.
You need to make up symbols for the radius of the disk and the current density. I recommend using a for the radius and sigma for the current density.
Consider a short segment of length `dr along a radial line, at average distance r * from the center.
What is the expression for the current moving across that segment?
That current continues in a circular path around the disk, forming a thin ring. This makes the thin ring equivalent to a circular wire. What is the expression for the magnetic field at its center?
The entire radial line, from its center where r = 0 to the outside of the disk where r = a, can be partitioned into such intervals. Each subinterval of this partition is like the one we analyzed, and makes its contribution to the magnetic field at the center. It is as though you had divided the disk into a large number of concentric circular wires. The total magnetic field would be approximated by a Riemann sum of contributions from all these intervals. As the partition grows finer and finer, the Riemann sum approaches and integral.
It is this integral that gives you the correct expression for the magnetic field.
*@
A square loop with area A and carrying current I lies initially stationary in a horizontal plane and is constrained to rotate about an axis parallel to two of its sides and passing through the center of the square. A vertical uniform magnetic field B permeates the region. If the loop has moment of inertia J, then what differential equation relates the angular position `theta of the loop to clock time?
@&
Assume first that the loop makes angle theta with the horizontal plane.
What is the direction of the force exerted by the magnetic field on the current in each of the sides of the square loop?
What is the magnitude of each of these forces?
Which of these forces, if any, produce a torque on the loop?
What therefore is the net torque on the loop?
For a rotating object, Newton's Second Law says that
net torque = moment of inertia * angular acceleration.
What is the net torque as a function of the angle theta?
What therefore is the acceleration of the loop as a function of theta?
Angular acceleration in this situation is theta ' ' , where ' represents derivative with respect to clock time and ' ' the second derivative.
So the differential equation is
moment of inertia * theta ' ' = net torque.
*@
** **
Listed above are two problems from practice tests for test 3. I don't even know where to begin for either one of them. If you could please explain how to work out these problems that'd be great. Thank you.
** **
How do I do these two problems?
@&
I've inserted some explanation. I'll be glad to look at your answers to these questions, or to answer additional questions.
*@