Magnetic field at center of half square

[HelpMeh]

Hi, I am having some trouble understanding the formula for the magnetic field for a straight wire.

The equation is:

B = (μ/4∏)(I/R)(sinθ₂ - sinθ₁)

the picture looks like this:

...___
__| . |____

with the current coming in from the left. To find the magnetic field at the point (middle) You need two angle, which is where the issue comes up. I am not sure which two angles to use.

What i know:

im pretty sure to find the magnetic field generated by the vertical sides you would sweep out an angle from 0 to 45° (from bottom of the side to the top). then multiply by 2 since both sides will create the same B field, i have no idea what to use for the top side, possibly angle 1 being 45 and angle 2 being 135, but you get zero if this is done.any help is appreciated.

 

[tiny-tim]

Hi HelpMeh!

Hi, I am having some trouble understanding the formula for the magnetic field for a straight wire.

The equation is:

B = (μ/4∏)(I/R)(sinθ₂ - sinθ₁)
…
im pretty sure to find the magnetic field generated by the vertical sides you would sweep out an angle from 0 to 45° (from bottom of the side to the top). then multiply by 2 since both sides will create the same B field, i have no idea what to use for the top side, possibly angle 1 being 45 and angle 2 being 135, but you get zero if this is done.

You're using the wrong θ …

θ for the closest point is 0, not 90° …

so your angles will be ±45° …

(and for an infinitely long wire would be ±90°)

i suggest you check this by applying the Biot-Savart law. ​

 

[Bob S]

Look at the fifth formula down in http://www.phys.uri.edu/~gerhard/PHY204/tsl216.pdf