A ring of mass m, radius R having charge q uniformly distributed over it and free to rotate about its own axis is placed in a region having a magnetic field B parallel to its axis. If the magnetic field is suddenly switched off, the angular velocity acquired by the ring is

Question

Infinity Learn · Accepted Answer

Consider a shaded ring of thickness dr , having small charge dq. $$dq=q$$$$π$$$$R22$$$$π$$rdr Induced electric field is $$E(say)$$ $$E2$$$$π$$$$r=$$π$$r2dBdt$$ ⇒$$E=r2dBdt$$ This electric field will apply force on charge dq, which will generate torque dτ. τ$$=$$∫dτ$$=$$∫$$rdF=$$∫$$rEdq=$$∫r×$$r2dBdt$$×q$$π$$$$R22$$$$π$$$$rdr=qR24$$△B△t We know,  Angular $$Impulse=$$△$$L=$$τ△t ⇒I△ω$$=qR24$$△B△t×△t ⇒$$mR22$$△ω$$=qR24$$△B ⇒△ω$$=qB2m$$

A ring of mass m, radius R having charge q uniformly distributed over it and free to rotate about its own axis is placed in a region having a magnetic field B parallel to its axis. If the magnetic field is suddenly switched off, the angular velocity acquired by the ring is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material