1.) Since the charge-to-mass ratio of the electron is known veryaccurately (1.75
ID: 1765129 • Letter: 1
Question
1.) Since the charge-to-mass ratio of the electron is known veryaccurately (1.759E11 C/Kg), the experiment you are about to do canbe used to measure the magnitude of a uniform magnetic field.Electrons are accelerated from rest through a potential differenceof 344 V. Then these electrons entera uniform magnetic field that is perpendicular to the their initialdirecton. Due to the interaction with the magnetic field, they movein a circular path of radius 0.741 cm.
a) What is the magnitude of the magnetic field?
1 mT
The magnetic field was generated by a Helmhotz coil pair likethe one described in the manual. You measure the coils anddetermine that the average diameter is 151 mm.
b) What is the magnitude of the current through the coils?
2 A
Assume a proton has a mass 1849 timesgreater than the electron. Its electric charge is the samemagnitude as that of the electron, but it is positive instead ofnegative.
c) What voltage would the proton have to be accelerated throughfor it to move in the same circle as the electron in parts a andb?
3 V
Explanation / Answer
q/m = 1.759E11 C/kg, V = 344 V, r = 0.741 m a) qV = mv2/2, so v = (2qV/m) qvB = mv2/r B = mv/(qr) = m(2qV/m) /(qr) = (2mV/q) /r =(2*344/1.759E11) /0.741 = 0.0844 mT b) d = 0.151 m, B = 0.81.5*20I/d I = 7.09 A c) for electron, B = (2mV/q) /r for proton, m' = 1849 m, need V' mV = m'V' V' = 0.186 V
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