An alpha particle is moving at a speed of 5 times 10^5 m/s in a direction perpen

Question

An alpha particle is moving at a speed of 5 times 10^5 m/s in a direction perpendicular to a uniform magnetic field of strength 4 times 10 T. The charge of an alpha particle is 3.2 times 10^-19 C and its mass is 6.6 times 10^-27 kg. (a) Determine the radius of the orbit of the alpha particle. (b) What is the time it takes the alpha particle to complete one revolution around as path? A 2-m long wire is carrying a current of 2 A. The wire is makes an angle of 60 degree with respect to a magnetic field. If the wire experiences a force of 0.2 N, what is the strength of the magnetic field? A straight wire carries a 12-A current eastward and a second straight wire carries a 14-A current westward. The wires are separated by a distance of 20 cm. What is the magnitude of the magnetic field produced by these two currents at a point midway between the wires?

Explanation / Answer

(A) magnetic force = centripetal force

q v B = m v^2 / r

r = m v / q B

= (6.6 x 10^-27) (5 x 10^5) / (3.2 x 10^-19 x 4 x 10^-2)

= 0.256 m

(B) t = 2 pi r / v

= 2 x pi x 0.256 / (5 x 10^5)

= 3.24 x 10^-6 sec

2:

F = IL X B = IL B sin(theta)

0.2 = 2 x 2 x B x sin60

B = 0.058 T

3: B = u0 I / ( 2 pi r)

B1 = (4pi x 10^-7 x 12) / (2 xpi x 0.10) = 2.4 x 10^-5 T

B2 = ( 4pi x 10^-7 x 14) / (2 x pi x 0.10) = 2.8 x 10^-5 T

B = B1 + B2 = 5.2 x 10^-5 T

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