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
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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 )
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