Magnitude of the magnetic field of a bar magnet that has a magnetic moment

In summary, a slender bar magnet with a magnetic moment of 5.50 A m2 is held at a 45 degree angle to a uniform magnetic field. When released, it rotates with an initial angular acceleration of 8.40×10^3 rad/s2. By setting the torque and moment of inertia equal to each other and solving for the magnetic field, we can find that the magnitude of the magnetic field is approximately 0.674 T.
  • #1
MarieWynn
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Homework Statement


A slender, 200- g bar magnet 15.0 cm long has a magnetic moment of 5.50 A m2. It is held at an angle of 45 o to the direction of a uniform magnetic field. When released, it begins to rotate about its center with an initial angular acceleration of 8.40×103 rad/s2. What is the magnitude of the magnetic field?


Homework Equations


T=torque
T=Ia
I=1/12mL^2
T=mu*B*sin(theta)


The Attempt at a Solution


Using the equations above, you can set Ia and mu*B*sin(theta) equal to one another and get: mu*B*sin(theta)=(mL^2/12)*a and then solve for B, which gives you:
B=(mL^2/12)*a/mu*sin(theta). Making the necessary conversions and plugging in the numbers from the question gives me:
B=(0.2*0.15^2/12)*8.4x10^3/5.5*sin(45)=0.673 T

I've gone over the problem multiple times and keep getting the same answer, which my homework is telling me is wrong. Did I miss a crucial step? Thanks!
 
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  • #2


Hi there, it looks like you have the right approach to the problem. However, I noticed a small mistake in your calculation. When plugging in the numbers, you should use the value of 8.40×10^3 for the angular acceleration, not 8.4. This small difference can lead to a slightly different answer. When I plugged in the correct value, I got a magnetic field of approximately 0.674 T. I hope this helps!
 

1. What is the formula for calculating the magnitude of the magnetic field of a bar magnet?

The formula for calculating the magnitude of the magnetic field of a bar magnet is B = μ0M/4πr^3, where B is the magnetic field, μ0 is the permeability of free space, M is the magnetic moment, and r is the distance from the magnet.

2. How is the magnetic moment of a bar magnet determined?

The magnetic moment of a bar magnet is determined by multiplying the strength of its poles by the distance between them. This can be represented mathematically as M = m x 2l, where m is the pole strength and 2l is the distance between the poles.

3. How does the distance from the bar magnet affect the magnitude of the magnetic field?

The magnitude of the magnetic field decreases as the distance from the bar magnet increases. This can be explained by the inverse square law, which states that the strength of a field is inversely proportional to the square of the distance from the source.

4. What is the unit of measurement for the magnetic field of a bar magnet?

The unit of measurement for the magnetic field of a bar magnet is Tesla (T) in the International System of Units (SI). It can also be measured in Gauss (G) in the cgs system.

5. Can the magnetic field of a bar magnet be changed?

Yes, the magnetic field of a bar magnet can be changed by altering its magnetic moment or by changing the distance from the magnet. It can also be changed by exposing the magnet to external magnetic fields or by heating it to a certain temperature known as the Curie temperature.

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