Differentiating Biot-Savart Law

[Eri ep]

Hello!

I have the equation F_M = 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=(μ_e/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!

 

[mfb]

What do you actually want to do?

Is this homework?

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.

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?