Magnetic field at center of half square

HelpMeh

Hi, im 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. Im 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!
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