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 1.0m and runs parallel to a wire that carries a 0.20 A current in the +x-direction. The beam is 10.0cm from the wire.

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

b) Find the deflection of the beam as it passes through the 1-m region by calculating the impulse 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) As velocity is in direction of flow of current.

So by using F= q(vxB)   

q=-e. By right hand thumb rule magnetic field acts out of the paper, velocity along the direction of current,so (vxB) comes toward right but as electron has negative charge it is reflected towards left I.e away from the wire

B) As magnetic force changes the direction of motion, not the initial velocity

Electron beam still moves with same velocity along x axis and travels 1 m

Time to travel 1 m = distance/velocity= 1/0.02c = 1/(0.02*3*10^8)= 16.67*10^(-8) sec

Force acting on electrons due to magnetic ffield = qvB = (1.6*10^-19)(0.02*3*10^8)(mu*I/2pi*d)

Substituting value of current I= 0.2 A and distance d = 0.1 and mu =4pi*10^-7

We get force = 3.84*10^-19 N

So acceleration = F/m = 3.84*10^-19/9.1*10^-31=4.23*10^11

So deflection y= ut + at^2/2. Initial velocity along the direction in which force is acting is zero

So. Y = 4.23*10^11(16.67*10^-8)^2/2 =587.7*10^-5 m = 0.05877 cm

C)yes it does changes as force due to magnetic field gives velocity in direction away from wire, while initial velocity in the direction of wire is still same 0.02c as magnetic force acts perpendicular to velocity, thereby electron has now velocity in both direction therefore kinetic energy increases

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.