# Magnetic Field square wire loop

• faen
In summary, the conversation discusses finding the approximate value of the magnetic field intensity at a point near a corner of a square wire loop with a current flowing through it. The proposed solution using Biot-Savart's law is incorrect and the correct formula should be used instead.
faen

## Homework Statement

A current I is flowing in a square wire loop of side a. Find the approximate value of the magnetic field intensity magnitude at the point P, which is near to one of the corners in the plane of the square at the same d distance from the near two sides! (d<<a).

## Homework Equations

I would guess biot and savarts law or formula of magnetic field on a straight current carrying conductor.

## The Attempt at a Solution

I thought like this: B=2*I*u0/(2*pi*d)=2I*u0/(pi*d). That would be twice the magnetic field of an infinite long current conducting wire. But that was wrong and I don't know why.. Any help would be greatly appretiated.

hi faen!

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faen said:
I thought like this: B=2*I*u0/(2*pi*d)=2I*u0/(pi*d). That would be twice the magnetic field of an infinite long current conducting wire.

ok, following that line of thought …

add an identical square loop, sharing that corner with the first loop

that's (effectively) two infinite straight wires, and so your formula would give the correct result for it

you now propose to divide by 2, but do you really think that the new square has as great a field at the given point as the old square?

start again, using the formula for a finite straight wire

(find that formula from the biot-savart law if you don't already know it)

## 1. What is a magnetic field square wire loop?

A magnetic field square wire loop is a configuration of wire where the length and width of the wire are equal, forming a square shape. When an electric current flows through the loop, it creates a magnetic field around the wire.

## 2. How does a magnetic field square wire loop work?

The flow of electric current through the loop causes the negatively charged electrons in the wire to move in a circular motion. This creates a magnetic field that is perpendicular to the plane of the loop. The strength of the magnetic field depends on the amount of current flowing through the wire and the distance from the wire.

## 3. What are the applications of a magnetic field square wire loop?

Magnetic field square wire loops have various applications in physics, engineering, and technology. They are used in motors, generators, transformers, and other electromagnetic devices. They are also used in scientific experiments to study the properties of magnetic fields.

## 4. How can the strength of a magnetic field square wire loop be increased?

The strength of a magnetic field square wire loop can be increased by increasing the amount of electric current flowing through the wire or by decreasing the distance from the wire. Additionally, using a material with a higher magnetic permeability, such as iron, can also increase the strength of the magnetic field.

## 5. Are there any safety precautions when working with a magnetic field square wire loop?

Yes, it is important to be cautious when working with a magnetic field square wire loop, especially when high currents are involved. The magnetic field can induce electric currents in nearby conductive materials, so it is important to keep other objects away from the loop. It is also important to use proper insulation and handle the wires carefully to avoid electric shocks.

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