A proton follows the path shown in the figure as it moves through three regions

Question

A proton follows the path shown in the figure as it moves through three regions with different uniform magnetic fields,B1 ,B2 , and B3. In each region the proton completes a half-circle, and the magnetic field is perpendicular to the page. Part A:Rank the three fields in order of decreasing magnitude.
Part B:Give the direction (into or out of the page) for the field B1.
Part C:Give the direction (into or out of the page) for the field B2.
Part D:Give the direction (into or out of the page) for the field B3.
Additional info. B1 is on the upper border of the page to the right B2 is in the middle of the page to the left B3 is lower border of page to the right. Roughly it looks like so _____>B1__
B2 <______ )
(_________>B3

Explanation / Answer

part A)

expression for the radius of the circle is

R=mv/qBsin.

This shows that if the speed, mass, and charge don’t change, the larger B will produce the smaller R because B is in the denominator. Smaller R means a “sharper” curve. So the sharpest curve will have the largest B.

part B, C and D)

The positively charged proton enters field B1 with a velocity pointing to the right. The magnetic force makes the proton curve down. So, use the RHR - point your fingers (velocity) to the right with your extended thumb (force) pointing down. Your palm faces out of the page (screen) so this must be the direction of B1. Now, you do the other two.

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