Motion of a Charged Particle in Magnetic Field

In summary, the strength of the magnetic field required to hold antiprotons moving at 5.0×107m/s in a circular path with a radius of 2.00 m is 0.26T, taking into account the mass, velocity, and charge of the antiprotons. The magnitude of the magnetic field is a positive number, so the absolute value should be used in the calculation.
  • #1
Ignitia
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Homework Statement


Viewers of Star Trek have heard of an antimatter drive on the Starship Enterprise. One possibility for such a futuristic energy source is to store antimatter charged particles in a vacuum chamber, circulating in a magnetic field, and then extract them as needed. Antimatter annihilates normal matter, producing pure energy. What strength magnetic field is needed to hold antiprotons, moving at 5.0×107m/s in a circular path 2.00 m in radius? Antiprotons have the same mass as protons but the opposite (negative) charge.

Homework Equations


F = ma = m * (v2/r)
F = qvB

The Attempt at a Solution


Okay, this is pretty straightforward:

v = 5.0x10-7 m/s
m = 1.672x10-27 kg
q = -1.6x10-19C
r = 2m

F = qvB
F/(qv) = B
[(m*(v2) / r ] * 1/(qv) = B
(mv/rq) = B

Plugging in the values, answer becomes - 0.26T, but the correct answer is 0.26T. What am I missing?
 
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  • #2
Strength of magnetic field is another name for magnitude which is a positive number.
 
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  • #3
kuruman said:
Strength of magnetic field is another name for magnitude which is a positive number.

So I just take the absolute value? That makes sense, thanks.
 

What is the motion of a charged particle in a magnetic field?

The motion of a charged particle in a magnetic field is circular. This is because the particle experiences a force perpendicular to its velocity due to the magnetic field.

How does the direction of the magnetic field affect the motion of a charged particle?

The direction of the magnetic field determines the direction of the force on the charged particle. If the magnetic field is parallel to the velocity of the particle, there will be no force and the particle will continue in a straight line. If the magnetic field is perpendicular to the velocity, the particle will experience a force perpendicular to both the velocity and the magnetic field, resulting in circular motion.

What is the formula for calculating the force on a charged particle in a magnetic field?

The formula for the force on a charged particle in a magnetic field is F = qvBsinθ, where q is the charge of the particle, v is its velocity, B is the strength of the magnetic field, and θ is the angle between the particle's velocity and the magnetic field.

How does the mass of the charged particle affect its motion in a magnetic field?

The mass of the charged particle does not affect its motion in a magnetic field. The force on the particle is dependent on its charge and velocity, but not its mass. Therefore, particles with different masses but the same charge and velocity will experience the same force and have the same circular motion in a magnetic field.

What is the difference between a uniform and a non-uniform magnetic field in relation to the motion of a charged particle?

In a uniform magnetic field, the strength and direction of the magnetic field is the same at all points. This results in a constant force on the charged particle, causing it to move in a circular path at a constant speed. In a non-uniform magnetic field, the strength and direction of the magnetic field varies at different points, resulting in a non-uniform force on the charged particle and potentially causing it to accelerate or decelerate in its circular motion.

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