# Magnetic field produced by a current

I'm translating the problem from portuguese to english, so I'm sorry if there are errors.

## Homework Statement

Determine the magnetic field on the center of the circumference produced by the current in the conducting wire (the circumference is made of conducting wire too). The current goes from left to right, and on the circumference it's clockwise.

## Homework Equations

Biot-Savart Law: $B = \frac{\mu_0}{4 \pi} \ \int \frac{ I \ \vec{dl}\times \hat{r}}{r^2}$

## The Attempt at a Solution

I can't relate dl with r (the distance from dl to the center) nor the angle, which I must do to compute the integral.

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berkeman
Mentor
I'm translating the problem from portuguese to english, so I'm sorry if there are errors.

## Homework Statement

Determine the magnetic field on the center of the circumference produced by the current in the conducting wire (the circumference is made of conducting wire too). The current goes from left to right, and on the circumference it's clockwise.

## Homework Equations

Biot-Savart Law: $B = \frac{\mu_0}{4 \pi} \ \int \frac{ I \ \vec{dl}\times \hat{r}}{r^2}$

## The Attempt at a Solution

I can't relate dl with r (the distance from dl to the center) nor the angle, which I must do to compute the integral.
The trick to this question is to see that the B field in the center of that loop is the sum of the B-field from the loop itself, plus the B-field from the long straight wire....

The trick to this question is to see that the B field in the center of that loop is the sum of the B-field from the loop itself, plus the B-field from the long straight wire....
yep the right hand rule can also gives a good indication as well

on the straight wire the current goes right so curling your fingers indicates the field points down. On The loop the current goes clockwise tot he magnetic field is again down.

For the long straight wire you must relate the center of the ring to a segment dl on the long straight wire that is a distance r1 away. which you can relate to theta by integrated from pi/2 to -pi/2 yep the right hand rule can also gives a good indication as well

on the straight wire the current goes right so curling your fingers indicates the field points down. On The loop the current goes clockwise tot he magnetic field is again down.

For the long straight wire you must relate the center of the ring to a segment dl on the long straight wire that is a distance r1 away. which you can relate to theta by integrated from pi/2 to -pi/2

View attachment 36832
So, dl = rdθ? And how do relate I r with θ?

berkeman
Mentor
So, dl = rdθ? And how do relate I r with θ?
Your book should have a solution for the B-field from a long straight wire. And a separate solution for the B-field at the center of a single loop of wire. Do you see how they set up the integrals for each of those...?