Q. 9  Excercises And Problems
ExpertverifiedElectrons pass through the parallel electrodes shown in FIGURE with a speed of . What magnetic field strength and direction will allow the electrons to pass through without being deflected? Assume that the magnetic field is confined to the region between the electrodes
The strength and direction of magnetic field is and out of page respectively.
We are given that
speed of electron is ,
potential difference between two plates is and
distance d between two plates is .
We need to find magnetic field strength and direction that will allow the electrons to pass through without being deflected.
Applying Newton's law of motion in y direction, we get
m= 
where is acceleration of electron in y direction, is electric force and is magnetic force on electron
According to question, electrons are passing without being deflected,
therefore, = 0
Substituting value of in equation , we get,
0 =
On solving,

From the definition of and
and
where q is charge of electron, E is electric field , v is velocity of electron and B is magnetic field.
Substituting value of and in equation , we get
qE = qvB
On solving,

Expression for electric field between two plates is

substituting equation in equation , we get
(5)
substituting the given values in equation (5), we get
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