Please provide necessary formulas and constants to solve problem and throughly e

Question

Please provide necessary formulas and constants to solve problem and throughly explain how to get solution to problem.

A 150 V battery is connected across two parallel metal plates of area 28.5 cm^2 and separation 8.20 mm. A beam of electrons is accelerated from rest through a potential difference of 1.75 kV and enters the region between the plates perpendicular to the electric field. What magnitude and direction of magnetic field are needed so that the electrons travel undeflected between the plates?

Explanation / Answer

Solution:

first of all calculate the speed (v) of electrons.

as it is accelerated by a potential difference of 1.75 kV, energy imaprted=1.75 keV

then

1/2*m*v^2=1.75 keV

v=2.48*10^7 m/s

electric field in the space between metal plates=(voltage/distance)=V/d=18292.68 V/m

the force on the elctron due to electric field will be

charge *electric field=2.926829*10^(-15) N

and in the opposite direction of the electric field

For electrons beam to travell undeflected, the force due to magnetic field should be such that it should balance the force due to electric field,

as here angle is 90 degree, magnitude is given by

q*v*B

where q=charge of electron

v=speed of electron

B=magnetic field strength

electrons will not deflect if,

Fe = FB

=>q*E = q*v*B

=>B = E/v

then putting values for all the parameters,

we get B=7.37*10^(-4) T

assuming the electric field in -ve z direction, speed of electron in +ve x direction,

we get B in -ve y direction.

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