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A charged particle has specific charge (charge-to-mass ratio) alpha. It starts from rest at the origin at t = 0 with initial velocity v0*i_hat + v0*j_hat in a uniform magnetic field B0*i_hat. Find the coordinates of the particle at time t = pi / (alpha * B0).
- (v0/(2*B0*alpha), sqrt(2)*v0/(alpha*B0), -v0/(B0*alpha))
- (-v0/(2*B0*alpha), 0, 0)
- (0, 2*v0/(B0*alpha), v0*pi/(2*B0*alpha))
- (v0*pi/(B0*alpha), 0, -2*v0/(B0*alpha))
Correct answer: (v0*pi/(B0*alpha), 0, -2*v0/(B0*alpha))
Solution
The x-motion is uniform (B along x does not affect vx), giving x = v0*pi/(alpha*B0). The initial y-component v0 and z-component 0 undergo circular motion with period 2*pi/(alpha*B0); at t = pi/(alpha*B0) (half period) the y-displacement returns to 0 and z-displacement = -2*v0/(alpha*B0).
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