An electron beam contains electrons that move along the +x-axis at 0.020c. The b

Question

An electron beam contains electrons that move along the +x-axis at 0.020c. The beam enters a region of length 1.0 m and runs parallel to a wire that carries a 0.20-A current in the +x-direction. The beam is 10.0 cm from the wire.

(a) Specify the direction in which the bea is deflected, if at all.

(b) Find the deflecton of the beam as it passes through the 1-m region by calculating the impilse it receives during its brief passage through that region.

(c) After it has passed the wire, does the beam have the same energy it had when it entered the region that contains the wire?

Explanation / Answer

a) if the beam is above +x axis it deflects upward

if the beam is below +x axis it deflects downward

b) assume B is constant in the path of electron beam.

B = mue*I/(2*pi*r) = 2*10^-7*0.2/0.1 = 4*10^-7 T

F = q*v*B*sin(90)

= 1.6*10^-19*0.02*3*10^8*4*10^-7

= 6.24*10^-19 N

a = F/m = 6.24*10^-19/9.1*10^-31 = 6.857*10^11 m/s^2

time taken to pass 1 m, t = d/v = 1/0.02*3*10^8 = 1.67*10^-7 s


deflection = 0.5*a*t^2

= 0.5*6.857*10^11*1.67^2*10^-14

= 9.523*10^-3 m

= 9.523 mm

c) The magnetic force does some work on electron beam so kinetic enrgy increases.

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