An electron is moving to the east at a speed of #1.8*10^6 m/s#. It feels a force in the upward direction with a magnitude of #2.2*10^-12N#. What is the magnitude and direction of the magnetic field this electron just passed through?

1 Answer
A08
May 16, 2018

Let us define coordinate system as below.
Let velocity of electron be #v_e=1.8xx10^6hati\ ms^-1#
Given force experienced by it #F_B=2.2xx10^-12hatj\ N#

From Lorentz Force equation we know that a charge #q# moving with velocity #vecv# passing through a magnetic field #vecB# experiences force given as

#F_B=q(vecvxxvecB)#

Inserting given values and taking charge of electron as #-1.602xx10^-17\ C# we get

#2.2xx10^-12hatj=-1.602xx10^-17(1.8xx10^6hatixxvecB)#
#=>|vecB|=(2.2xx10^-12)/(1.602xx10^-17xx1.8xx10^6)#
#=>|vecB|=0.076\ T#
Direction of the magnetic field is given as of #hatk# as
#hatj=-(hatixxhatB)#

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