# Magnetic field using Biot-Savart's Law

• K.QMUL
In summary, the conversation discusses the use of Biot-Savart's law to show that the magnetic field at the center of an infinitely long hollow cylinder with a constant current is zero. The attempt at a solution suggests using a symmetry argument and imagining the cylinder as an infinite number of wires to understand the cancellation of magnetic fields.
K.QMUL

## Homework Statement

An in finitely long hollow cylinder of radius a carries a constant current I. Use Biot-Savart's law
and show that the magnetic field at the centre of the cylinder is zero.

## Homework Equations

Biot-Savart's law

## The Attempt at a Solution

I cannot seem to come up with anything meaningful. I have tried searching this question but it seems the best way is normally to use Ampere's law and not Biot-Savarts law. Could someone explain the steps or show the steps how we could use Biot-Savart's law in this case.

This is really just a symmetry argument. Think about sitting between two wires that have current flowing in the same direction. You know the magnetic field from one wire (using the Biot-Savart law), and you know it is going to cancel that of the other wire in the middle. Now just line the surface of a cylinder with an infinite number of these wires and you have your problem, but you get the same result.

## 1. What is Biot-Savart's Law?

Biot-Savart's Law is a fundamental law in electromagnetism that describes the relationship between a steady electric current and the resulting magnetic field. It was first discovered by Jean-Baptiste Biot and Félix Savart in the early 19th century.

## 2. How is Biot-Savart's Law used to calculate magnetic fields?

Biot-Savart's Law states that the magnetic field at a point in space due to a steady current can be calculated by integrating over the contributions of infinitesimal segments of the current. This means that the magnetic field is directly proportional to the current and inversely proportional to the distance from the current.

## 3. What is the difference between Biot-Savart's Law and Ampere's Law?

Biot-Savart's Law is used to calculate the magnetic field due to a steady current, while Ampere's Law is used to calculate the magnetic field due to a steady current enclosed by a closed path. Biot-Savart's Law takes into account the contributions of all segments of the current, while Ampere's Law only takes into account the current enclosed by the path.

## 4. Can Biot-Savart's Law be applied to non-steady currents?

No, Biot-Savart's Law only applies to steady currents. For non-steady currents, the more general form of the law, known as the Ampere-Maxwell Law, must be used.

## 5. How is Biot-Savart's Law used in real-world applications?

Biot-Savart's Law is used in many real-world applications, such as determining the magnetic field around a wire carrying a current, designing electromagnets, and calculating the strength of magnetic fields in motors and generators. It is also used in medical imaging techniques such as MRI machines.

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