# Magnetic field of 2 infinite wires.

• dikmikkel
In summary, using Amperes' law, the field strength for two thin, long wires carrying equal and opposite currents situated in y = -a and y = a is found to be B(y) = \dfrac{\mu_0 I}{2\pi (a-y)}. The average field strength in a region -b to b is found to be 0, which may seem incorrect but is in fact correct due to the equal and opposite currents canceling out.

## Homework Statement

Two thin, long wires situated in y = -a and y = a carrying two equal in magnitude and opposite running currents I.
Find the field strength in therms of y.
Find the average Field strength in a region -b to b, where 0 is between the 2 points.

Amperes law.

## The Attempt at a Solution

I find via. Amperes' law, that the field of the wire in -a (current running down) has the magnitude:
$B(y) = \dfrac{\mu_0 I}{2\pi r_1}$
Where r1 is the distance from the wire, now i find that r1 = a-y.
The field from the other is the same with the distance r2 instead of r1. r2 = a-y too so the field is zero and the average is of course also 0, and that is annoying. What have i done wrong.

Last edited by a moderator:
Better check if, for the downgoing wire, r1 = a - y.

## What is the magnetic field of 2 infinite wires?

The magnetic field of 2 infinite wires is the region surrounding the wires where magnetic forces are exerted on other objects. It is created by the flow of electric current through the wires.

## How is the magnetic field of 2 infinite wires calculated?

The magnetic field of 2 infinite wires can be calculated using the Biot-Savart law, which states that the magnetic field at a point is directly proportional to the current in the wire and inversely proportional to the distance from the wire.

## What factors affect the strength of the magnetic field of 2 infinite wires?

The strength of the magnetic field of 2 infinite wires is affected by the distance between the wires, the amount of current flowing through the wires, and the orientation of the wires relative to each other.

## Can the magnetic field of 2 infinite wires be manipulated?

Yes, the magnetic field of 2 infinite wires can be manipulated by changing the distance between the wires, altering the amount of current flowing through the wires, or by introducing other objects into the magnetic field.

## What are some real-world applications of the magnetic field of 2 infinite wires?

The magnetic field of 2 infinite wires has many practical applications, including in motors, generators, transformers, and various types of electronic devices. It is also used in medical imaging techniques such as magnetic resonance imaging (MRI).