Magnetic field with a split current

[bfusco]

Homework Statement

A circular conducting ring of radius R is connected to two exterior straight wires at two ends of a diameter. The current I splits into unequal portions while passing through the ring. What is the magnitude of B at the center of the ring?

The Attempt at a Solution

My problem isn't with solving the question, it's with which equation to use. i originally did it using the equation finding B in a wire B=μI/2∏R, however that is apparently the incorrect equation. the equation is B=μI/4R, i don't know what the equation is, and considering the problem is of a current carrying wire that splits into 2 wires (where the current is distributed unequally) then reconnects to form a single wire again. i would think you would use the equation to find B in a wire.

If someone could explain why i am suppose to use the B=μI/4R equation and what it is i would appreciate it so much.

 

[anathema]

Hello, thank you for your question. The equation B=μI/4R is the correct equation to use in this scenario. This is known as the Biot-Savart law, which is used to calculate the magnetic field at a certain point due to a current-carrying wire. The reason this equation is used instead of the one you mentioned (B=μI/2∏R) is because the wire in this problem is not a straight wire, but rather a circular ring. The Biot-Savart law takes into account the geometry of the wire, which in this case is a circular loop.

In order to use the Biot-Savart law, you will need to integrate over the length of the wire to take into account the unequal distribution of current. This will result in the final equation B=μI/4R, where R is the radius of the circular loop. I hope this helps clarify why the Biot-Savart law is used in this scenario. Let me know if you have any further questions.