A proton moves in the magnetic field B ? =0.50 i ^Twith a speed of 1.0107m/s in

Question

A proton moves in the magnetic field B?  =0.50i^Twith a speed of 1.0107m/s in the directions shown in the figure. For each, what is magnetic force F?  on the proton?

Part A

Express vector F? in the form Fx, Fy, Fz, where the x, y, and z components are separated by commas.

Part B

Express vector F? in the form Fx, Fy, Fz, where the x, y, and z components are separated by commas.

A proton moves in the magnetic field B? =0.50i^Twith a speed of 1.0 107m/s in the directions shown in the figure. For each, what is magnetic force F? on the proton? Part A Express vector F? in the form Fx, Fy, Fz, where the x, y, and z components are separated by commas. Part B Express vector F? in the form Fx, Fy, Fz, where the x, y, and z components are separated by commas.

Explanation / Answer

Answer

The formula for the force on a particle in a magnetic field is F = q*v x B. F is the force, q is the charge, v is the velocity and is a vector, and B is the magnetic field and is a vector, x is the cross product. Hopefully you know how to do a cross product, or at least how to use the right hand rule. I'm assuming B = .50i is in units of Teslas (T).

F = qv x B is equivalent to qvBsin(?), where ? is the angle between the direction of the velocity and the direction of the magnetic field, and instead of vectors you only use the scalar value (the magnitude of the vector). The charge of a proton is 1.602*10^-19 C.

a) F = qvBsin(?) = (1.602*10^-19 C) (1.0*10^7 m/s) (.50 T) sin (45 degrees) = 5.66*10^-13 N.

Now you need to know the direction to give the vector components. Use the right hand rule for this (if you don't know it, google image search it and you will be able to figure it out). The cross product also points parallel to both of the vectors that you took the cross product of. Therefore F points into the page, which is the positive y direction. Therefore the vector components of F are [Fx, Fy, Fz] = [0, 5.66*10^-13 N, 0].

b) Using F = qvbsin(?), you can see that ? is 180 degrees, and sin(180 degs) is 0. Therefore F = 0, and [Fx, Fy, Fz] = [0,0,0].

I am a physics major and I'm pretty sure I did this correctly.

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