Magnetic field created in a perpendicular point

[heruh4ra]

Homework Statement

The idea is that we have a current in a wire, and the B magnetic field is to be known in a specific point P. This point P is in the same straight line as the part of the wire we are interested in.

For example, in the attached image the problem would be to know the field that is created by "side A" which is in the same axis as point "P", in this point "P".

Homework Equations

Biot&Savart

dB = (u_0 / 4π) * (I dl x [r vector] / r^2)

The Attempt at a Solution

dB = (u_0 / 4π) * (I dl sin(θ) / r^2)

Since θ is the angle between [r vector] and dl and this angle θ=0 degrees, sin(0) = 0, so there is no magnetic field at P created by side A from the current

 

[anathema]

in side A.


Thank you for sharing your thoughts on this problem. I agree with your attempt at a solution using the Biot-Savart law. However, I would like to point out that the angle θ should be between the [r vector] and the direction of current, rather than the [r vector] and dl. This means that θ=0 degrees in this case, as dl and the direction of current are parallel.

Additionally, I would like to mention that the Biot-Savart law only gives the magnitude of the magnetic field, not the direction. In order to determine the direction of the magnetic field at point P, we would need to use the right hand rule or the right hand grip rule, depending on the orientation of the wire and the direction of the current.

I hope this helps clarify the solution to this problem. Keep up the good work in your studies!