Finding Magnetic Field of Alpha Particle in a Circle

In summary, an alpha particle with a non-relativistic speed is moving at a constant speed in a circle perpendicular to a uniform magnetic field. The magnitude of the magnetic field can be calculated using the equation T= 2(pi)m / qB, where m is the mass of the alpha particle, q is its charge, and T is the time it takes to make one revolution (60 nanoseconds in this case). The radius of the circle is not given and is not needed to solve the question. The force acting on the alpha particle is equal to the centripetal force, which is also equal to the magnetic force. By equating these forces, we can solve for the magnetic field. The calculated value for the magnetic field is
  • #1
howt
11
0

Homework Statement



An alpha particle is moving at constant speed in a circle, perpendicular to a uniform magnetic field, making a revolution every 60 nanoseconds.
Its speed is non-relativistic

What is the numerical magnitude of the magnetic field in T ?


Homework Equations


alpha particle (2 protons + 2 neutrons)

We have here T= 2(pi)m / qB

in which
m=Mass (alpha particle= 6.64*10^-27) kg
q=Charge = 2(1.6*10^-19) C
T= (60*10^-9) s

The Attempt at a Solution



This should be just plugging in, I got 2.1729, yet it is wrong...
Why?
 
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  • #2
What is the radius of the circle?
 
  • #3
it is not given...

I don't think we need it to solve the question
The formula of it doesn't involve any radius...
 
  • #4
howt said:
it is not given...

I don't think we need it to solve the question
The formula of it doesn't involve any radius...
When the alpha particle is moving ina circle, what is the force acting on it?
What is the force on alpha particle due to the magnetic field?
 
  • #5
The Centripetal force is going to equal the magnetic force.

Note that w = v/r

Centripetal force , F=m v^2 /r..
=m r w^2

And the magnetic force on the alpha particle is, F = B q v
= B q w r

m r w^2 = B q w r
m w = B q

in which w= 2(pi) / T

Thus T= 2(pi)m / qB
 
  • #6
Your answer appears to be correct.
 
  • #7
Thanks, the problem might be those constant...

Side Note: I just realize I got a typo on the topic... crap
 

FAQ: Finding Magnetic Field of Alpha Particle in a Circle

What is the purpose of finding the magnetic field of an alpha particle in a circle?

The purpose of finding the magnetic field of an alpha particle in a circle is to understand the behavior and interactions of charged particles in a circular motion when exposed to a magnetic field. This can help in various fields such as particle physics, electromagnetism, and nuclear physics.

How can the magnetic field of an alpha particle in a circle be calculated?

The magnetic field of an alpha particle in a circle can be calculated using the formula B = (mu_0 * q * v) / (2 * pi * r), where B is the magnetic field, mu_0 is the permeability of free space, q is the charge of the alpha particle, v is its velocity, and r is the radius of the circle.

What factors affect the magnetic field of an alpha particle in a circle?

The magnetic field of an alpha particle in a circle is affected by the strength of the external magnetic field, the charge and velocity of the particle, and the radius of the circular path.

What is the direction of the magnetic field of an alpha particle in a circle?

The direction of the magnetic field of an alpha particle in a circle is perpendicular to both the velocity of the particle and the radius of the circular path. It follows the right-hand rule, where the thumb points in the direction of the velocity and the fingers curl in the direction of the magnetic field.

How does the magnetic field of an alpha particle in a circle affect its motion?

The magnetic field of an alpha particle in a circle causes a force on the particle, known as the Lorentz force, which causes it to change direction and stay in a circular motion. This force is perpendicular to both the velocity and the magnetic field, and its magnitude is dependent on the charge and velocity of the particle.

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