Question

a) What is the radius of the circular path of a charge of 29.2 x 10^-6 C and a mass of 2.29 x 10^-9 kg moving with a speed of 517 m/s perpendicular to magnetic field with a magnitude of 0.28 ?

b) A positive charge of 327.3 x 10^-6 C is moving perpendicular to a uniform magnetic field of 1,940 T. What is the magnitude of the magnetic force exerted on this charge if its speed is 0.41 m/s?

c) A positive charge traveling with a speed of 10,142 m/s enters the deflection chamber of a mass spectrometer. In the deflection chamber exists a uniform magnetic field of 0.6 T. The charge undergoes a deflection with a radius of curvature that is 0.024 m. If the charge is 1.602 x 10^-19 C, what is its mass in atomic mass units*?

*1 Amu = 1.66 x 10^-27 kg

d) A particle with a positive charge of 29.4 x 10^-6 C is traveling at a constant rate of 77,037 m/s. It enters a uniform magnetic field of 3 T that is directed at an angle of 14 degrees with respect to the direction that the charge is moving. What is the magnitude of the magnetic force exerted on this charge?

Answer 1

Multiple questions posted, so answering only the first question:

For uniform circular motion,centripetal force = mv2/r, where m is mass, v is velocity and r is radius.

Also, magnetic force on a moving charge=qvB sin, where q is charge,v is velocity, B is magnetic field and is the angle between velocity and magnetic field.

Here,=90 degrees. So, magnetic force = qvB sin90 = qvB.

Magnetic force provides the necessary centripetal force.

So, qvB=mv2/r

=>r=mv/(qB).

Here, m= 2.29 x 10-9 kg , v=517 m/s, q= 29.2 x 10-6 C ,B=0.28 T.

So,r= 2.29 x 10-9*517/(29.2 x 10-6 * 0.28) = 0.1448 m.

So,required radius=0.1448 m.