Electrons are moving in a uniform magnetic field on a circular path with radius

Question

Electrons are moving in a uniform magnetic field on a circular path with radius R.   

a) When the magnetic field is decreased, the new radius will ?

   i) decrease (ii) increase (iii) stay the same

b) When the electrons are ejected with higher speeds from the electron gun, is the radius of their paths...?

   i) greater (ii) smaller (iii) the same

c) Now consider a magnetic field which is uniform in space but decreases at a constant rate. This changing magnetic field induces an electric field.

   i) Which equation describes this phenomenon and is useful to answer part (ii)

   ii) The induced electric field is

   - increasing in time

   - decreasing in time

   - is conservative

   - is in opposite direction to the magnetic field

   - has a constant magnitude

Explanation / Answer

If the charge moving in the magnetic field , magnetic force on the charge is                 F = Bqv Centripetal force on the charge is                 F = mv2 / R Since the centripetal force balanced by magnetic force, then              Bqv = mv2 / R                  R = mv / Bq (a) from above equation, radius wiil be increases when the magnetic filed decreased (b) Radius of path in directly praportional to the velcoity of the electron.      so the radius of paths greater than the initial. (c)Change in magentic field induces the current as well as voltage.     This induced voltage gives induced electric field.        From Faraday's law induced emf is                     V = - d(B.A)/dt    Electric field is E = Vd                              =  - A*d* dB/dt    Since the magnetic field decreases with time, incued electric field decrases with time.                      

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