### Unveiling the Magnetic Force Between Parallel Conductors

Explore the practical and theoretical significance of understanding the magnetic force between parallel conductors, crucial for electromagnetism and modern technology.

**Ampère's law**,

\[\nabla\times\mathbf{B}\left(\mathbf{r}\right)=\mu_{0}\mathbf{j}\left(\mathbf{r}\right)\]

relates the **magnetic induction** \(\mathbf{B}\left(\mathbf{r}\right)\) to the **current distribution** \(\mathbf{j}\left(\mathbf{r}\right)\).

In this section we will learn the basic techniques to calculate the magnetic induction for a given current distribution. We will use integral methods like the law of **Biot-Savart** or differential methods for certain symmetries to solve Ampère's law directly.

Explore the practical and theoretical significance of understanding the magnetic force between parallel conductors, crucial for electromagnetism and modern technology.

Published
in
Electrodynamics /
Magnetostatics /
Currents and Magnetic Fields

Tags: Superposition Principle

Tags: Superposition Principle

What happens if we take a wire, drill a hole in it and set some current in motion? Will we encounter a magnetic field?

Published
in
Electrodynamics /
Magnetostatics /
Currents and Magnetic Fields

Tags: Rotational Symmetry / Cylindrical Coordinates / Ampere's law / Stoke's theorem / Biot-Savart's law

Tags: Rotational Symmetry / Cylindrical Coordinates / Ampere's law / Stoke's theorem / Biot-Savart's law

The magnetic field of a thin and infinitely long wire is calculated using Biot-Savart's law.

Published
in
Electrodynamics /
Magnetostatics /
Currents and Magnetic Fields

Tags: Rotational Symmetry / Cylindrical Coordinates / Ampere's law / Stoke's theorem / Biot-Savart's law

Tags: Rotational Symmetry / Cylindrical Coordinates / Ampere's law / Stoke's theorem / Biot-Savart's law

We calculate the magnetic field of a wire with constant current. Using symmetries we verify the right-hand rule.

Published
in
Electrodynamics /
Magnetostatics /
Currents and Magnetic Fields

Tags: Rotational Symmetry / Cylindrical Coordinates

Tags: Rotational Symmetry / Cylindrical Coordinates

The magnetic field for a current distribution in form of a cylinder shell is determined.

Published
in
Electrodynamics /
Magnetostatics /
Currents and Magnetic Fields

Tags: Biot-Savart's law / Taylor Expansion

Tags: Biot-Savart's law / Taylor Expansion

Helmholtz coils are a devices that can provide a very homogeneous magnetic field. Let's find an approximation for their magnetic field!

Through physical reasoning we find that the spin of the electron cannot be explained by a classical rotation.