Calculating Magnetic Moment of Rotating Charge

In summary, the magnetic moment associated with a rotating charged particle can be calculated by multiplying the charge by half of the angular velocity and the square of the radius. The formula for this is M=q(omega/2)*(r^2).
  • #1
blueyellow

Homework Statement


A particle of charge q is rotating in a circular orbit of radius r with angular velocity omega. determine the magnetic moment associated with the motion of the charge


Homework Equations


M=IS



The Attempt at a Solution


M=I*(pi*r^2)
hav no idea how to get rid of the 'I' in the equation tho. its an 8 mark question so mayb it involvs something complicated

thanks in advance
 
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  • #2
for a rotating charged particle, current I = q.f, where, q = charge, f = frequency of rotation.
 
  • #3
you have r and omega, so you can find f.
 
  • #4
why do i need r to find f? isn't omega just 2 pi f?
 
  • #5
yes right. you don't need r. so did you get the answer?
 
  • #6
M=qf*(pi*r^2)
M=q(omega/2pi)*(pi*r^2)
M=q(omega/2)*(r^2)
?
 
  • #7
right.
 

1. What is the formula for calculating the magnetic moment of a rotating charge?

The formula for calculating the magnetic moment of a rotating charge is μ = qvr, where μ is the magnetic moment, q is the charge, v is the velocity, and r is the distance from the center of rotation.

2. How does the direction of rotation affect the magnetic moment?

The direction of rotation does not affect the magnitude of the magnetic moment, but it does determine the direction of the magnetic moment vector. The vector points in the direction of the axis of rotation according to the right-hand rule.

3. Can the magnetic moment of a rotating charge be negative?

Yes, the magnetic moment of a rotating charge can be negative. This occurs when the direction of the charge's velocity is opposite to the direction of its rotation, resulting in a negative vector for the magnetic moment.

4. How does increasing the charge affect the magnetic moment?

Increasing the charge increases the magnetic moment proportionally. This means that a charge with double the magnitude will have a magnetic moment that is also twice as large.

5. Is there a relationship between the magnetic moment and the strength of the magnetic field?

Yes, there is a direct relationship between the magnetic moment and the strength of the magnetic field. The stronger the magnetic moment, the stronger the resulting magnetic field will be.

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