lorentz force (1 Viewer)

bleakarcher · Aug 2, 2012

If an electron enters an electric and magnetic field and is not deflected by the two fields, determine:
a) What can be said about the forces on the electron
b) What are the direction of the electric and magnetic fields that produce a result such as in part a)
c) If the electric field has a strength of 100N/C and the magnetic field has a strength of 0.3T, what is the speed of the electron?

SpiralFlex · Aug 2, 2012

bleakarcher said:
If an electron enters an electric and magnetic field and is not deflected by the two fields, determine:
a) What can be said about the forces on the electron
b) What are the direction of the electric and magnetic fields that produce a result such as in part a)
c) If the electric field has a strength of 100N/C and the magnetic field has a strength of 0.3T, what is the speed of the electron?

$a) The force acting on the electron by the electric field is balanced by the magnetic field.$

$$b) The magnetic field is situated perpendicularly to the electric field. Hence$ \;F_{E}=F_{B}$

$So let's consider if a positive potential was at the top of the plate and a lower potential on the bottom.$

$Field lines run from top to bottom. So if I move the electron into the field, it will effectively be attracted to the positive plate. However, we said the forces need to be balanced. So we need a downward force. How do we provide this downward force to the electron? By utilising a magnetic field and orientating it such that the force is downwards.$

$By the right hand palm rule, palms face down, thumb points in opposite direction of the electron movement. Your 4 fingers (hopefully 4) will point into the page.$

$Hence our magnetic field points into the page.$

$Combing the two, we can let the electron pass being undeflected.$

$c) F_{E}= qE$

$F_{B}=qvB\sin \theta$

$$Since,$\; F_{E}=F_{B}$

$qE=qvB\sin \theta$

$E=vB\sin \theta$

$Now since there is perpendicularity between the magnetic field and the electron, theta is equal to 90.$

$\therefore E=vB ($This equation is used in one of Thomson's experiments of C-T-M ratio.)$$

$100=v*0.3$

$v=\frac{100}{0.3}\;ms^{-1}$

bleakarcher · Aug 2, 2012

Thanks Spiral

lorentz force (1 Viewer)

bleakarcher

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SpiralFlex

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bleakarcher

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