A uniform magnetic field exists in a region of space. Two experiments were done

Question

A uniform magnetic field exists in a region of space. Two experiments were done to discover the direction of the field and the following results were obtained. A proton moving to the right with instantaneous velocity v1 experienced a force F1 directed into the page, as shown above. A proton moving out of the page with instantaneous velocity V2 experienced a force F2 in the plane of the page as shown above. State the direction of the magnetic field and show that your choice accounts for the directions of the forces in both experiments. In which experiment did the proton describe a circular orbit? Explain your choice and determine the radius of the circular orbit in terms of the given force and velocity for the proton and the proton mass m. Describe qualitatively the motion of the proton in the other experiment.

Explanation / Answer

1) In experiment 1

We use the right hand rule to determinate the direction of the magnetic field

Remeber that:
F = qv x B

Velcoity to the left and force into the page so the magnetic field is downward

In experiment 2:

Velocity is out of the page and the force is in the plane with a 30 degree angle, so the magnetic field is in the plane with a angle 60 below the horizontal.

2) In both cases the the velocity is perpendicular to the magnetic field so it trajectory is circular

qvB = mv²/R

R = mv/qB

3) same as above.

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