# Solving Ampere's Law Trouble: My Mistake in Calculating B?

In summary, Ampere's Law, also known as the Ampere-Maxwell Law, is an equation in electromagnetism that relates the magnetic field around a closed loop to the electric current passing through the loop. To use it, you need to determine the current passing through the loop and integrate the magnetic field along its path. The most common mistake when using this law is not accounting for the direction of the magnetic field. To avoid mistakes, it is important to carefully determine the direction and double-check calculations. Some practical applications of Ampere's Law include designing electronic circuits, calculating magnetic fields, and understanding magnetic materials.

Where is my mistake? I have a feeling it's in the calculation of B... ?

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Do you mean that B is constant inside the rectangle?

ehild

It's a given that the rectangle is fixed to the ground..

So apart from the fact that the magnetic field in it changes direction all the time, B's size is constant

So you say that the magnetic field of a current carrying wire does not depend on the distance from the wire?

ehild

For a long straight wire, B is proportional to 1/r.

## 1. What is Ampere's Law?

Ampere's Law, also known as the Ampere-Maxwell Law, is one of the equations in electromagnetism that relates the magnetic field around a closed loop to the electric current passing through the loop. It is used to calculate the magnetic field generated by a current-carrying wire or a solenoid.

## 2. How do you use Ampere's Law to solve for B?

To use Ampere's Law, you need to determine the current passing through a closed loop and then integrate the magnetic field along the path of the loop. This will give you the total magnetic field at a specific point in space. If the current is constant, you can simplify the equation to B=μ0I/2πr, where μ0 is the permeability of free space, I is the current, and r is the distance from the wire.

## 3. What is the mistake commonly made when using Ampere's Law?

The most common mistake when using Ampere's Law is not properly accounting for the direction of the magnetic field. The direction of the field is determined by the right-hand rule, where your thumb points in the direction of the current and your fingers curl in the direction of the magnetic field.

## 4. How do you avoid making mistakes when using Ampere's Law?

To avoid mistakes when using Ampere's Law, it is important to carefully determine the direction of the magnetic field and make sure it is consistent throughout the calculation. It is also helpful to double-check your calculations and use multiple methods to verify your results.

## 5. What are some practical applications of Ampere's Law?

Ampere's Law has many practical applications, including designing and analyzing electronic circuits, calculating the magnetic field of a solenoid or electromagnet, and understanding the behavior of magnetic materials. It is also used in various technologies such as motors, generators, and transformers.

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