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Grade: 12


a proton of charge e and mass m enters a uniform magnetic field B=bî with an initial velocity v=vxî+vyj(cap).find an expression in unit-vector notation for its velocity at time t.

11 years ago

Answers : (1)

Askiitians Expert Bharath-IITD
23 Points
							Dear Padyot,
 We know the formula for the Force experienced by a charged particle moving with some velocity in a magnetic field

As F = q{ V cross B )
Where V and B are in vector notations.
after Calculations we get F = {q * [(-Vy)*b]} k
Where k is  a unit vector in z direction.
And the acceleration in z direction is given by 
a= (Force in z direction)/mass of the charge = (q/m) * [(-Vy)*b]
We know the equation of motion as v = u + a*t
And the initial velocity in z direction is zero
and thus velocity after time t seconds in z direction is given by
Vz = a*t
 Thus the velocity vector after time t seconds is given by

V = Vx i + Vy j + Vz k
  = Vx i + Vy j - { (q/m) * (Vy)*b } k

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Askiitians Experts
Adapa Bharath
11 years ago
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