A negative charge of q = -5.5 Ý 10-17C and m = 8.6 Ý 10-26 kg enters a magnetic

Question

A negative charge of q = -5.5 Ý 10-17C and m = 8.6 Ý 10-26 kg enters a magnetic field B = 1.4 T with initial velocity v = 430 m/s, as shown in the figure. The magnetic field points into the screen

a)Express the magnitude of the magnetic force, F, in terms of q, v, and B.

Part (c) Calculate the magnitude of the force F, in newtons.

Part (e) Express the centripetal acceleration of the particle in terms of the force F and the mass m.

Part (f) Calculate the magnitude of a, in meters per square second.

Part (g) Express the radius, R, of the circular motion in terms of the centripetal acceleration a and the speed v.

Part (h) Calculate the numerical value of the radius R, in meters.

Explanation / Answer

a. F = qvB sin theta

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c. F = -5.5e-17* 430* 1.4 = 3.311*10^-14 N

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e. a = F/m

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f. a = 3.311e-14/8.6e-26 = 3.85*10^11 m/s^2

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g. apply centripetal force = magnetic force

i.e mv^2/r = qvB,

where m = mass o the charged particle

v = velocity,   r = radius ,

q = charge = 1.6*10^-19 C

B = magnetic field

so now , r = mv/qB

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R = 8.6e-26 * 430/(5.5e-17 *1.4)

R = 0.480 um

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