Q. 63.9( 12 Votes )

When a proton is released from rest in a room, it starts with an initial acceleration a0 towards west. When it is projected towards north with a sped v0, it moves with an initial acceleration 3a0 towards west. Find the electric field and the minimum possible magnetic field in the room.

Answer :


Given-


Proton is released from rest in a room, it starts with an initial acceleration a0 towards west


Now, we know coulomb’s force F given by –




where


q = charge


E= electric field


Also,



And Newton's second law of motion



Where


m = mass


a= acceleration







From (1) and (2)



Electric field,



which acts towards west.


We know, Lorentz force F is given by -



where,


q = charge


v = velocity of the charge


B=magnetic field


and


and θ = the angle between B and l


Now, given that when the proton is projected towards north with a speed v0, it moves with an initial acceleration 3a0 towards west.





An electric force will act on the proton in the west direction, which produces an acceleration a0 on the proton.


Initially the proton was moving with velocity v, so a magnetic force was also acting on the proton.


So, magnetic force acting will be the only cause behind the change in acceleration of the proton



Change in acceleration towards west due to the magnetic force acting on it is -



∆a = 3a0a0 = 2a0



So from (2), the force will become -




Hence, required magnetic field



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