A proton (q = 1.6 X 10 -19 C, m = 1.67 X 10 -27 kg) moving with constant velocit

Question

A proton (q = 1.6 X 10-19 C, m = 1.67 X 10-27 kg) moving with constant velocity enters a region containing a constant         magnetic field that is directed along the z-axis at (x,y) = (0,0) as shown.  The magnetic field extends for a distance D = 0.72 m in the x-direction.  The proton leaves the field having a velocity vector (vx, vy) = (5.3 X 105 m/s, 3.7 X 105 m/s).

1) What is v, the magnitude of the velocity of the proton as it entered the region containing the magnetic field?         

m/s

2) What is R, the radius of curvature of the motion of the proton while it is in the region containing the magnetic field?         

m

3) What is h, the y co-ordinate of the proton as it leaves the region conating the magnetic field?         

m

4) What is Bz, the z-component of the magnetic field?  Note that Bz is a signed number.         

T

5)

A proton (q = 1.6 X 10-19 C, m = 1.67 X 10-27 kg) moving with constant velocity enters a region containing a constant magnetic field that is directed along the z-axis at (x,y) = (0,0) as shown. The magnetic field extends for a distance D = 0.72 m in the x-direction. The proton leaves the field having a velocity vector (vx, vy) = (5.3 X 105 m/s, 3.7 X 105 m/s).

Explanation / Answer

q = 1.6 X 10^-19 C, m = 1.67 X 10^-27 kg, D = 0.72 m,
(vx, vy) = (5.3 X 105 m/s, 3.7 X 105 m/s).

1) What is v, the magnitude of the velocity of the proton as it entered the region containing the magnetic field?
v = sqrt(vx^2 + vy^2) = 6.4 X 10^5 m/s

2) What is R, the radius of curvature of the motion of the proton while it is in the region containing the magnetic field?
R = D/sin(theta), where tan(theta) = vy/vx
R = 1.24 m

3) What is h, the y co-ordinate of the proton as it leaves the region conating the magnetic field?
R - h = D/tan(theta) = D*vx/vy
so h = 0.20 m

4) What is Bz, the z-component of the magnetic field? Note that Bz is a signed number.
Bz = mv/(qR) = 5.38*10^-3 T

5) If the velocity were increased, the radius of curvature would increase by the same factor since R is proportional to v. If the radius of curvature increases, the angle through which the particle bends in a distance D also decreases. If the angle decreases, then the displacement h also decreases.

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