Magnetic field/circular motion equation derivation

In summary, the formula to derive f=BQ/2pim is to use the equation F=BQv, where F is the centripetal force, B is the magnetic field, Q is the charge of the particle, and v is the velocity of the particle. Rearranging to solve for v and substituting it into the equation F=mv2/r will give the final formula of F=BQ/2pir.
  • #1
Hannah7h
40
0
How would you derive f=BQ/2pim ?

I've got as far as F=BQv, but now I don't know which centripetal force equation to use; either F=mv2/r or F=mw2r

Update: no worries I've done it
 
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  • #2
now. The answer is F=BQv, where F is the centripetal force, B is the magnetic field, Q is the charge of the particle, and v is the velocity of the particle. Rearranging to solve for v gives v=F/BQ, then substituting this into F=mv2/r gives F=(m/r)(F/BQ)2, which can be rearranged to F/BQ=2pirm, and finally F=BQ/2pir.
 

1. What is the equation for calculating the magnetic field in circular motion?

The equation for calculating the magnetic field in circular motion is B = μ0(I/2πr), where B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the radius of the circular path.

2. What is the significance of the magnetic field in circular motion?

The magnetic field in circular motion is significant because it is responsible for the force that keeps charged particles moving in a circular path. Without this force, the particles would continue in a straight line.

3. How is the magnetic field in circular motion derived?

The magnetic field in circular motion can be derived using the formula for the magnetic force on a charged particle moving in a magnetic field (F = qvB sinθ) and the centripetal force formula (F = mv²/r). By equating these two forces, we can solve for the magnetic field and derive the equation.

4. What is the role of the magnetic field in circular motion in electromagnets?

In electromagnets, the magnetic field in circular motion is crucial for creating a strong magnetic field. By passing a current through a coiled wire, a magnetic field is generated around the wire, and when this wire is bent into a circular shape, the magnetic field becomes concentrated in the center, making it stronger.

5. How does the magnetic field in circular motion affect the speed of charged particles?

The magnetic field in circular motion has no effect on the speed of the charged particles, but it does change the direction of their motion. The particles will continue to move at a constant speed, but their direction will constantly change as they move around the circular path.

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