Electron moving in magnetic field. (Physics 2, non calc)

[pdeco1]

Homework Statement

Electrons are fired Eastward at a certain location near Earth's surface. Ignore gravity.
A. Describe the motion of the electrons and describe the trajectory they follow.
B. If the electrons first return to their initial positions after 1.5 x 10^-6 seconds, determine the magnitude of the Earth's magnetic field.
C. If it is known that the horizontal component of the magnetic field is 1.9x10^-5 T. In precisely which direction should the electrons be fired so as to travel in a straight line? You may express any angle as an inverse trigonometric function.

Homework Equations

r=mv/qB

The Attempt at a Solution

A. The perpendicular magnetic force acts as centripetal force which keeps the particle in rotation around the Earth changing its direction but not velocity.

B. t= 1.5x10^-6 s, t = (2)(pi)(m)/qB, Solving for B = 2.38x10^-5 T

C.The "horizontal component" is tripping me up. Is there two magnetic fields here? One from the Earth and one from the moving electron?

 

[tiny-tim]

hi pdeco1!

A. The perpendicular magnetic force acts as centripetal force which keeps the particle in rotation around the Earth changing its direction but not velocity.

so the shape of the motion is … ?

C.The "horizontal component" is tripping me up. Is there two magnetic fields here? One from the Earth and one from the moving electron?

no, the Earth's magnetic field is at an angle to the horizontal, different in different places on the Earth …

see http://en.wikipedia.org/wiki/Magnetic_dip" for details

 

[pdeco1]

A. The path is circular.

Can you offer more advice on part C. My diagram has electron heading east, with the force downwards and the magnetic field rotating in and out of the page, which makes it horizontal to the earth.

While the electron is perpendicular to the Earth it with experience a centripetal force, the force is greatest at 90, and decreases as the angle between the path and the magnetic field decreases. Does the electron need to be fired vertically at 90 degrees to travel in a straight line?

 

[tiny-tim]

hi pdeco1!

A. The path is circular.

yup! (or helical )

While the electron is perpendicular to the Earth it with experience a centripetal force, the force is greatest at 90, and decreases as the angle between the path and the magnetic field decreases. Does the electron need to be fired vertically at 90 degrees to travel in a straight line?

the only path that isn't helical is a path parallel to the field

 

[pdeco1]

I understand the theory, but I am not sure how to figure out the angles. Any help would be appreciated.

Thanks.

 

[pdeco1]

The key to the problem was understanding that "horizontal" meant a uniform north field.

Set up the magnetic field values along an xy plane and use SOHCAHTOA to find the angle. The north(horizontal) value is given, combined with the magnetic field calculated from part B and the problem is easily solved.