A beam of protons traveling at 1.70 k m / s enters a uniform magnetic field, tra

Question

A beam of protons traveling at 1.70km/s enters a uniform magnetic field, traveling perpendicular to the field. The beam exits the magnetic field, leaving the field in a direction perpendicular to its original direction (the figure (Figure 1) ). The beam travels a distance of 1.10cm while in the field.

What is the magnitude of the magnetic field?

A beam of protons traveling at 1.70km/s enters a uniform magnetic field, traveling perpendicular to the field. The beam exits the magnetic field, leaving the field in a direction perpendicular to its original direction (the figure (Figure 1) ). The beam travels a distance of 1.10cm while in the field. What is the magnitude of the magnetic field?

Explanation / Answer

The beam moves in circular motion while in the field, so ittravels a quarter circle. The distance then is a quarter of thecircumference, or

dist = (1/4) 2?r

0.011 = (1/2) 2 ?r

r = 0.00700 m

Then the B field can be found by

F = q vB and F = m v2 / r

m v2 / r = q vB B = m v / qr

B = 1.67 x 10-27 * 1700 / 1.60 x10-19 * 0.00700 =

= 2.54 x 10-3 Tesla

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