17. Figure 1 below shows a schematic representation of the experiment used to de

Question

17. Figure 1 below shows a schematic representation of the experiment used to determine the charge to mass ratio (e/m) of the electron. The magnetic field produced by the Helmholtz coils is B 0.00147 T (pointing out of the page) and the electron beam follows a counter clockwise trajectory or radius r-0.0365 m. Figure 2 is a schematic of the "electron gun" used to accelerate the electrons. What value of the potential difference was used to accelerate electrons if the e/m ratio determined in the experiment is 1.74-10" C/kg? Figure 1. Figure 2. (electron gun) Helmholtz coils Tube Beam (counter clockwise trajectory) electron gun (see Figure 2.) Magnetic field D pointing out of page: a) 200 V b) 300 V c) 350V d) 250 V

Explanation / Answer

Using Force balance on electrons:

Fc = Fm

m*v^2/r = q*v*B

v = q*B*r/m

q = e

B = 0.00147 T

r = 0.0365 m

e/m = 1.74*10^11 C/kg

So, Speed of electron will be

v = 1.74*10^11*0.00147*0.0365

v = 9.336*10^6 m/sec

Now Using energy conservation

dPE = dKE

q*dV = m*vf^2/2 - m*vi^2/2

vi = 0 m/sec

vf = v = 9.336*10^6 m/sec

dV = (m/q)*Vf^2/2

Using known values

dV = (9.336*10^6)^2/(2*1.74*10^11)

dV = 250.46 V

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