Question

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 speed v0 it moves with an initial acceleration 3a0 towards west. find the electric field and the maximum possible magnetic field in the room

Answer 1

case 1 :

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

F₁ = electric force acting on the proton in west direction

q = charge on proton

E = electric field in the region in west direction

m = mass of proton

electric force on the proton can be given as

F₁ = qE

using newton's second law

F₁ = m a₀

hence

m a₀ = qE

E = m a₀/q

Case 2:

v₀ = initial velocity of the particle

F₂ = magnetic force acting on the proton in west direction

electric force + magnetic force on proton =  3 m a₀

F₁ + F₂ = 3 m a₀

m a₀ + F₂ = 3 m a₀

F₂ = 2 m a₀

maximum magnetic force is given as

F₂ = q v₀ B

so q v₀ B = 2 m a₀

B = 2 m a₀/(q v₀ )