# Magnetic field produced by a current

• Tosh5457
In summary: 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.
Tosh5457
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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Tosh5457 said:
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...

berkeman said:
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

Liquidxlax said:
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?

Tosh5457 said:
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...?

## What is a magnetic field produced by a current?

A magnetic field produced by a current is a region of space where a magnetic force is exerted on a charged particle or moving electric charge. It is created when an electric current flows through a wire or conductor.

## How is a magnetic field produced by a current measured?

A magnetic field produced by a current can be measured using a device called a magnetometer. This device can detect and measure the strength and direction of a magnetic field.

## What factors affect the strength of a magnetic field produced by a current?

The strength of a magnetic field produced by a current is affected by several factors, including the amount of current flowing through the wire, the distance from the wire, and the material the wire is made of. The strength of the magnetic field also decreases as you move further away from the current-carrying wire.

## What is the right-hand rule in relation to a magnetic field produced by a current?

The right-hand rule is a way to determine the direction of the magnetic field produced by a current. If you point your thumb in the direction of the current flow, then your fingers will point in the direction of the magnetic field lines.

## Can a magnetic field produced by a current be used for practical purposes?

Yes, a magnetic field produced by a current has many practical applications. It is used in motors, generators, and transformers, as well as in medical devices like MRI machines. It is also used in compasses, speakers, and many other everyday devices.

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