A) A proton of charge +1.60×10-19 C and mass 1.67×10-27 kg is introduced into a

Question

A) A proton of charge +1.60×10-19 C and mass 1.67×10-27 kg is introduced into a region of B = 0.135 T with an initial velocity of 1.10×106 m/s perpendicular to B. What is the radius of the proton's path?

Answer = 8.50×10-2 m

B) Suppose the initial velocity of the proton makes an angle of 50 deg with the direction of the magnetic field B. What is the pitch of the helix that describes the path of the proton? The pitch is the distance the proton travels along the axis of the helix in the time required for the proton to make one complete loop around the axis.

Please help with part B and show your work, thanks!

Explanation / Answer

when the velocity makes an angle of 50 degree with the magnetic field,

then component of velocity parallel to magnetic field will cause the pitch and component perpendicular will caose circular motion

pitch = vcos50 x time taken to complete on revolution

F = qvBsin50

m(vsin50)2/r = qvBsin50

r = mvsin50/qB

r = [1.67 x 10-27 x 1.1 x 106 x sin50]/[1.6 x 10-19 x  0.135]

r = 6.51 x 10-2

vsin502/r = 2r

= vsin50/r

= 1.1 x 106 sin50/(6.5 x 10-2)

= 1.3 x 107 rad/s

hence T = 2/

T = 4.83 x 10-7 s

pitch = vcos50 x T

pitch = 1.1 x106 x cos50 x 4.83 x10-7

pitch = 0.3415m

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