Effect of Earth's B field on an e/m experiment

[omicgavp]

I am doing an experiment to measure the charge to mass ratio of an electron. And I have found the method suggested by Thompson to account for the effect of the Earth's magnetic field[http://ajp.aapt.org/resource/1/ajpias/v58/i10/p1019_s1?isAuthorized=no" ]. But it only gives the equation, i.e. B_total=B_coils+B_earth, when the Earth's B field is (anti)parallel to the field from the coils. How about when the Earth's B field is oriented at an angle to the B field from the coils? Can you suggest journals or textbook references that mentions this case?

 

[jtbell]

How about when the Earth's B field is oriented at an angle to the B field from the coils?

The magnetic field \vec B is a vector quantity. Do you know how to add vectors?

 

[omicgavp]

The magnetic field \vec B is a vector quantity. Do you know how to add vectors?

If I solve for the vector sum of B_earth and B_coils, I would obtain a different direction for the total magnetic field which is contrary to that of the supposed circular path of the e- beam, i.e. B_total should be perpendicular to both F_m and v.

 

[jtbell]

When B is not perpendicular to v, you don't get a circular path. Think of v as having components perpendicular and parallel to B. The perpendicular component of v tends to produce circular motion, but the parallel component of v "carries" this circular motion along the direction of B, so you get a helical path whose axis is parallel to B. See this page for example:

http://farside.ph.utexas.edu/teaching/302l/lectures/node73.html

He calls the path a "spiral" which I consider to be incorrect terminology. To me, a "spiral" has a steadily decreasing radius so the path "shrinks" towards the center. And his picture looks more like a sine-wave than a spiral, but that's surely merely a matter of the crudeness of the drawing.

 

[YPelletier]

A while ago, I made an animation showing the helicoidal motion of a charged particle in a uniform magnetic field (when B is not perpendicular to v):

http://bestphysicsvideos.blogspot.com/2011/01/charged-particle-in-magnetic-field.html

Hope this helps.

When B is not perpendicular to v, you don't get a circular path. Think of v as having components perpendicular and parallel to B. The perpendicular component of v tends to produce circular motion, but the parallel component of v "carries" this circular motion along the direction of B, so you get a helical path whose axis is parallel to B. See this page for example:

http://farside.ph.utexas.edu/teaching/302l/lectures/node73.html

He calls the path a "spiral" which I consider to be incorrect terminology. To me, a "spiral" has a steadily decreasing radius so the path "shrinks" towards the center. And his picture looks more like a sine-wave than a spiral, but that's surely merely a matter of the crudeness of the drawing.