Differentiating Biot-Savart Law

In summary, the conversation discusses the equation FM = qvBsinθ and how to determine the minimum B value needed to change θ slightly. The individual is attempting to use differentiation to find this value and is seeking advice on how to eliminate variables and solve for dθ. They also mention being a high school senior taking Calculus BC and needing help on a time limit.
  • #1
Eri ep
3
0
Hello!

I have the equation FM = qvBsinθ .
As the end result, I am trying to figure out what B I need to change θ even a little bit. To do that, I was planning to find the minimum B by differentiating B=(μe/4π)(qv x R / R3) in terms of R and setting it equal to zero. . I am assuming that this is a form of the Biot Savart Law for things that aren't necessarily wires. Am I on the right track?

If I am on the right track, let's say I plug in the minimum B value I find into the very first equation. I now have three variables: θ, F, and dR or R. I'm confusing myself here... ignoring the F for now, I am trying to find dθ, if so, any tips on how to get rid of all the variable except for one? (I have q and v and μ as all constants).

I'm not at all knowledgeable on this topic, but since I'm on a time limit, jumping quite a bit. I'm a high school senior taking Calculus BC, so I can probably figure out the math... I hope :)

Thank you so much for helping!
 
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  • #2
What do you actually want to do?

Is this homework?
Eri ep said:
I am trying to figure out what B I need to change θ even a little bit
What does that mean? θ is the angle between motion and the magnetic field. It depends on the particle flying around. This angle, plus the velocity and the magnetic field, determine the force.

Eri ep said:
I was planning to find the minimum B by differentiating B=(μe/4π)(qv x R / R3)
That formula is at least missing an integral, but I don't think it is really doing what you want. Differentiating it with respect to what, to do what?
 

1. What is the Biot-Savart Law?

The Biot-Savart Law is a fundamental law in electromagnetism that describes the magnetic field generated by a steady electric current. It was first discovered and formulated by French physicists Jean-Baptiste Biot and Félix Savart in the early 19th century.

2. How does the Biot-Savart Law differ from Ampere's Law?

Ampere's Law and the Biot-Savart Law are both used to calculate the magnetic field produced by a steady current. However, Ampere's Law is based on the symmetry of the current distribution, while the Biot-Savart Law takes into account the individual contributions of each current element.

3. What are the limitations of the Biot-Savart Law?

The Biot-Savart Law is only applicable to steady currents and cannot be used for time-varying currents. It also assumes that the current is confined to a thin wire or filament, and does not take into account the effects of the magnetic field on the current itself.

4. How can the Biot-Savart Law be used to calculate the magnetic field of a current-carrying wire?

To calculate the magnetic field of a current-carrying wire using the Biot-Savart Law, the wire is divided into small segments and the contribution of each segment to the overall field is calculated using the formula. The contributions from each segment are then summed to find the total magnetic field at a given point.

5. Can the Biot-Savart Law be applied to non-linear materials?

No, the Biot-Savart Law is only valid for linear materials, which have a constant relationship between the magnetic field and the applied current. Non-linear materials, such as ferromagnetic materials, have a more complex relationship and require different equations to calculate the magnetic field.

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