An electron entersa magnetic fieldof 0.6 T, moving perpendicular to itwith a spe

Question

An electron entersa magnetic fieldof 0.6 T, moving perpendicular to itwith a speed of 7·105 m/s.

1.) Find the radius of the orbit it willmake.
2.) If the magnetic field pointsdirectly away from you (into the page), then this orbit would be inwhich direction from your perspective? a.)clockwise b.)counterclockwise c.) notenough info
If an electron weresent at the same speed, but at an angleof 40o to the magnetic field:

3.) What would be the radius ofthe helical motion?
4.) How long would it take for the electron totravel 3 m along ("downstream" to) the magneticfield?

5.) In general, will an electronneed to always travel in the same direction as ("downstream" to)the magnetic field?
Thank you for yourhelp!
2.) If the magnetic field pointsdirectly away from you (into the page), then this orbit would be inwhich direction from your perspective? a.)clockwise b.)counterclockwise c.) notenough info
If an electron weresent at the same speed, but at an angleof 40o to the magnetic field:

3.) What would be the radius ofthe helical motion?
4.) How long would it take for the electron totravel 3 m along ("downstream" to) the magneticfield?

5.) In general, will an electronneed to always travel in the same direction as ("downstream" to)the magnetic field?
Thank you for yourhelp!

Explanation / Answer

1.)The force experienced by the electron travelling in themagnetic field is F = q * v * B * sin The magnetic force on the electron is balanced by thecentripetal force on the electron therefore we get (m * v2/r) = q * v * B * sin or r = (m * v/q * B * sin) ----------(1) where m = 9.1 * 10-31 kg,v = 7 * 105m/s,q = 1.6 * 10-19 C,B = 0.6 T and =90o 2.)When the magnetic field points directly away from you (intothe page),then this orbit would be in the counterclockwisedirection.This is according to Ampere's right hand thumbrule.According to this rule,when the current flowing through a wireis indicated by the thumb of the right hand,then the curling offingers of the right hand indicate the direction of the magneticfield. 3.)The radius of the helical motion is equal to the valueobtained from equation (1). 4.)Let the time taken by the electron to travel 3 m along("downstream" to) the magnetic field be t.The speed of the electronis v = (2r/t) or t = (2r/v) 5.)In general,the electron need not always travel in the samedirection as ("downstream" to) the magnetic field.This is becausethe electron usually travels in a direction perpendicular to themagnetic field. 2.)When the magnetic field points directly away from you (intothe page),then this orbit would be in the counterclockwisedirection.This is according to Ampere's right hand thumbrule.According to this rule,when the current flowing through a wireis indicated by the thumb of the right hand,then the curling offingers of the right hand indicate the direction of the magneticfield. 3.)The radius of the helical motion is equal to the valueobtained from equation (1). 4.)Let the time taken by the electron to travel 3 m along("downstream" to) the magnetic field be t.The speed of the electronis v = (2r/t) or t = (2r/v) 5.)In general,the electron need not always travel in the samedirection as ("downstream" to) the magnetic field.This is becausethe electron usually travels in a direction perpendicular to themagnetic field.

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