A proton enters a magnetic field of 5 T and follows a spiral trajectory with a pitch of 5 cm. The angle θ between the velocity vector (v) and the magnetic field vector (B) can be determined using the equations F = B q v sin θ and F = m v² / r. The pitch of the spiral is defined as the vertical distance traveled after one complete revolution, which is calculated as vcosθ multiplied by the time period for one revolution (T). To solve for θ, additional information such as speed or radius is required.
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Basic_Physics said:That is it went 5 cm up or down after one revolution.
apelling said:The pitch of a spiral is the distance moved after one complete revolution.
The diagram in section 2.5 of this wiki article is fairly clear:-
http://en.wikipedia.org/wiki/Screw_thread
The two velocity components would be
vsinθ perpendicular to B
vcosθ parallel to B
vsinθ should be used in both the equations you give not just the first one.
The two forces can then be equated.
The pitch of the spiral is equal to vcosθ x (time period for one revolution, T) ie distance=speed x time
But T also is equal to 2πr/vsinθ.
Using the above ideas I found an expression for θ that still had one unknown in it. Is there any other information given in the question?