I could use some help on this one. Thank you!! *19.8 GEOMAGNETISM: THE EARTH MAG

Question

I could use some help on this one. Thank you!! *19.8 GEOMAGNETISM: THE EARTH MAGNETIC FIELD 51. . (a) Exiting from a small Exiting from a small linear accelerator near Wash- ington D.C., a proton is moving parallel to the ground What should the direction(s) of its velocity be in ord maximize the upward component of the Earth's force on it? (b) Using a value of 0.05 mT for the the horizontal component of the Earth's magnetic field at this location, what is the upward acceleration of the proton as it exits the accelerator at a speed of 2000 m/s? alue of

Explanation / Answer

51a )

B = magnetic field

q = charge on proton

F = magnetic force component in upward direction

v = speed of proton along horizontal direction

magnetic force is given as

F = q (v x B)

to increase the component of magnetic force, the velocity "v" can be increased as the force is directly propotional to the velocity "v"

b)

B = magnetic field = 0.05 x 10-3 T

v = 2000 m/s

q = charge = 1.6 x 10-19 C

magnetic force is given as

F = q v B

F = (1.6 x 10-19) (2000) (0.05 x 10-3 )

F = 1.6 x 10-20 N

m = mass = 1.67 x 10-27 kg

acceleration is given as

a = F/m = (1.6 x 10-20)/(1.67 x 10-27) = 9.6 x 106 m/s2

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