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3 years ago

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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. T

he 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}?

1 answer:

Usimov [2.4K]3 years ago

6 0

Answer:

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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<em>A satellite in outer space is moving at a constant velocity of 21.4 m/s in the y direction when one of its onboard thruster turns on, causing an acceleration of 0.250 m/s2 in the x direction. The acceleration lasts for 45.0 s, at which point the thruster turns off. </em>

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$a_{x}$ - Acceleration in +x direction, measured in meter per square second.

$t$ - Time, measured in seconds.

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