A beam of protons is accelerated through a potential difference of 0.725kV and then enters a uniform magnetic field traveling perpendicular to the field.
What magnetic field would be needed to produce a path with the same diameter (1.76m) if the particles were electrons having the same speed as the protons?
qV=.5mv^2
(1.6x10^-19)(725) = .5(9x10^-31)v^2
16062378.4 = v
1.76m / 2 = 0.88m
so....
B = (9x10^-31)(16062378.4) / (1.6x10^-19)(0.88)
B = 0.000102671 T
But this is wrong. I did the same thing but with protons and it was correct.
What magnetic field would be needed to produce a path with the same diameter (1.76m) if the particles were electrons having the same speed as the protons?
qV=.5mv^2
(1.6x10^-19)(725) = .5(9x10^-31)v^2
16062378.4 = v
1.76m / 2 = 0.88m
so....
B = (9x10^-31)(16062378.4) / (1.6x10^-19)(0.88)
B = 0.000102671 T
But this is wrong. I did the same thing but with protons and it was correct.
-
When you wrote:
"qV=.5mv^2
(1.6x10^-19)(725) = .5(9x10^-31)v^2"
you used the mass of the electron (9x10^-31kg - which should have been 9.11x10^-31kg by the way).
But the electrons are not accelerated through 725V - that's the protons. You should have used the mass of the proton.
So you have mixed up data for the electrons and data for the protons. in the same equation.
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First find the speed of the protons:
qV=.½mv²
(1.6x10^-19)(725) = ½ x (1.67x10^-27) x v²
v² = 1.389x10^11
v = 3.727x10^5 m/s
___________________________________
Now you find the magnetic field needed to make electrons of the same speed travel in a circle radius r=1.76/2 = 0.88m:
Magnetic force = centripetal force
Bqv = mv² /r
B = mv/(qr)
= (9.11x10^-31) x (3.727x10^5) / ((1.6x10^-19) x 0.88)
= 2.41x10^-6 T
"qV=.5mv^2
(1.6x10^-19)(725) = .5(9x10^-31)v^2"
you used the mass of the electron (9x10^-31kg - which should have been 9.11x10^-31kg by the way).
But the electrons are not accelerated through 725V - that's the protons. You should have used the mass of the proton.
So you have mixed up data for the electrons and data for the protons. in the same equation.
___________________________________
First find the speed of the protons:
qV=.½mv²
(1.6x10^-19)(725) = ½ x (1.67x10^-27) x v²
v² = 1.389x10^11
v = 3.727x10^5 m/s
___________________________________
Now you find the magnetic field needed to make electrons of the same speed travel in a circle radius r=1.76/2 = 0.88m:
Magnetic force = centripetal force
Bqv = mv² /r
B = mv/(qr)
= (9.11x10^-31) x (3.727x10^5) / ((1.6x10^-19) x 0.88)
= 2.41x10^-6 T