Consider a particle with a charge-to-mass ratio of ?/? = 1moving in a uniform magnetic field of B = 1 Tesla applied inz-direction. At time t = 0 s, it is located at r = (0, 10, 0) m andits velocity is v = (10, 0, 0) m/s.
(a) Qualitative motion
Draw a diagram of the situation when the proton starts itsmotion, showing its instantaneous velocity v0, the magnetic fieldvector B and the direction of the initial force F0 on theproton.
Describe how the velocity of the proton will change as itmoves through the magnetic field. Describe changes, if any, in boththe magnitude and direction of the velocity.
Describe the path the proton will follow in going through thisuniform magnetic field.
Calculate the speed v of the proton. Â Â
[8 marks]
(b) Quantitative motion
Determine the magnetic force acting on the protoninitially.
Find the radius of the circular path the proton follows interms of its charge q, mass m and speed v, and the strength of themagnetic field B. Then, calculate the numerical value of thatradius for the proton.
Determine the time required and the angular frequency for onecomplete revolution.
[6 marks]
(c) Deriving equations of motion
Starting with the magnetic force on the particle and usingNewton's second law to write down the differential equations forthe components ax , ay and az of the acceleration a acting on theparticle.
Describe the motion of the particle in z-direction if theinitial velocity component in that direction vz is not zero.Describe how the overall motion of the particle changes in thatcase .
[6 marks]
