Question

Let's say that you are given a magnetic field
B = 0.00109[Tesla].
You also have an
average V / d² = 25989[V/m²];
what is the value for e / m ?

Answer 1

This question has given very less details about the situation, I'm assuming standard situation where an electron starts from rest and passes through potential difference and enter into a magnetic field, In this case

When electron passes through potential difference, then using energy conservation:

dKE = dPE

(1/2)*m*v^2 = e*V

v = speed of electron when it enters into magnetic field

V = potential difference

v = sqrt (2*e*V/m)

Now when it enters into magnetic field then it will move in circular motion due to magnetic force on it, So

Fc = Fm

m*v^2/d = e*v*B

v = e*d*B/m

So from both equations:

sqrt (2*eV/m) = e*d*B/m

square on both sides

2*e*V/m = e^2*d^2*B^2/m^2

e/m = 2*V/(B^2*d^2)

Given that B = 0.00109 T

V/d^2 = 25989 V/m^2

So,

e/m = 2*25989/(0.00109^2)

e/m = 4.37*10^10 C/kg

where C/kg is units of e/m

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