An alpha particle (mass 6.64 times 10^-27 kg and charge + 2e) is moving in a reg

Question

An alpha particle (mass 6.64 times 10^-27 kg and charge + 2e) is moving in a region of uniform 0.140 T magnetic field at a speed of 2.86 times 10^6 m/s. Determine the radius of the circular motion of the alpha particle? What is the frequency of the circular motion of the alpha particle? A 0.137 T magnetic field is directed out of the page as shown in the following diagram. Tow rails are separated by 13.8 cm, connected at one end with a 5.25 Ohm resistor. A bar is free to move along the rails. At what speed and direction should the bar move such that a current of 75.7 mA is directed upward through the resistor.

Explanation / Answer

7)

a) For circular motion,

Magnetic force = m v^2 / r

q v B = m v^2 / r

r = m v / q B

r = (6.64 x 10^-27 x 2.86 x 10^6 ) / (2 x 1.6 x 10^-19 x 0.104 )

r = 0.571 m

b) frequency = v / (2 pi r )

= (2.86 x 10^6) / (2 x pi x 0.571) =7.98 x 10^5 Hz

8) induced emf = i R = 75.7 x 10^-3 x 5.25 = 0.397 V

induced emf, e = B L v

0.397 = 0.137 x 0.138 x v

v = 21.02 m/s

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