A particle that has mass m and charge q enters a uniform magnetic field that has magnitude B and is directed along the x axis. The initial velocity of the particle is in the xy plane.

a) Describe the particle's path as it travels through the magnetic field.

b) If the particle enters the magnetic field at t = 0, what is its angular displacement at t=2{eq}\pi {/eq}m/qB? Express your answer in terms of some or all of the variables m, q, B, and the constant {eq}\pi {/eq}?

a) The trajectory will be a helical path.

b) θ = 2*π rad

Explanation:

a) Since the initial velocity of the particle has a component parallel (x-component) to the magnetic  field B , the trajectory will be a helical path.

b) Given

t = 2*π*m/(q*B)

We can use the equation

θ = ω*Δt

where

θ is the angular displacement

ω is the angular speed, which is obtained as follows:

ω = q*B/m

then we have

θ = (q*B/m)*2*π*m/(q*B)

⇒  θ = 2*π rad

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