TEORIA Il flusso del campo magnetico AMALDI ZANICHELLI

Summary

This script explains the concept of magnetic flux in the International System of Units, where it is measured in Weber (Tesla times square meters). The magnetic flux through a surface is compared to electric flux, highlighting the absence of isolated magnetic monopoles in nature. Gauss's theorem for magnetism is introduced, which states that the total magnetic flux through a closed surface is zero. The script then demonstrates this theorem using an infinite straight wire with current, showing how magnetic field lines are concentric circles around the wire and why the flux through a cylindrical Gaussian surface is zero.

Takeaways

• 😀 Magnetic flux in the International System (SI) is measured in Weber (Wb), equivalent to Tesla (T) multiplied by square meters (m²).
• 😀 The concept of magnetic flux is similar to electric flux, where the flux of an electric field through a closed surface is proportional to the total charge enclosed.
• 😀 Unlike electric charges, isolated magnetic monopoles (north or south poles) have never been observed in nature.
• 😀 When a magnet is divided into smaller parts, each part retains both a north and a south pole, indicating the absence of isolated poles.
• 😀 Magnetic field lines are always closed loops or extend infinitely, meaning they do not have a starting or ending point like electric field lines.
• 😀 Each magnetic field line crosses any Gaussian surface twice: once entering and once exiting.
• 😀 Gauss's law for magnetism states that the total magnetic flux through a closed surface is zero, reflecting the absence of magnetic monopoles.
• 😀 To verify Gauss's law for magnetism, consider the magnetic field of an infinite straight wire carrying a current.
• 😀 In the case of a current-carrying infinite straight wire, the magnetic field lines form concentric circles around the wire.
• 😀 The total magnetic flux through a cylindrical Gaussian surface around the wire is zero because the flux through the lateral surface and the two bases of the cylinder is zero, due to the perpendicular nature of the magnetic field to the surface.

Q & A

What unit is used to measure magnetic flux in the International System of Units?

Magnetic flux is measured in Weber (Wb), which is equivalent to Tesla multiplied by square meters (T ⋅ m²).

How is magnetic flux analogous to electric flux?

Magnetic flux is defined in a similar manner to electric flux. Just as the electric flux through a surface is proportional to the enclosed electric charge, magnetic flux is calculated in a similar way but does not involve isolated magnetic charges.

Can magnetic monopoles exist in nature?

No, magnetic monopoles have never been observed in nature. Even if a magnet is divided into smaller parts, each piece will still have both a north and a south pole.

What is the shape of magnetic field lines?

Magnetic field lines are closed loops, or in some cases, extend infinitely. They always form continuous, closed curves or open-ended lines, depending on the context.

What does Gauss's theorem for magnetism state?

Gauss's theorem for magnetism states that the total magnetic flux through any closed surface is zero, meaning there are no net magnetic charges within the surface.

How is the validity of Gauss's theorem for magnetism verified?

The validity of Gauss's theorem for magnetism can be verified by considering the magnetic field produced by an infinitely long straight wire carrying a current. The magnetic flux through a Gaussian surface, such as a cylindrical surface around the wire, is zero.

What is the configuration of magnetic field lines around an infinitely long straight wire carrying current?

The magnetic field lines around an infinitely long straight wire carrying a current form concentric circles centered on the wire.

What type of Gaussian surface is chosen to verify Gauss's theorem for magnetism in the case of a current-carrying wire?

A cylindrical Gaussian surface is chosen, with its axis aligned with the wire. This choice simplifies the calculation of the magnetic flux through the surface.

Why is the magnetic flux through the lateral surface of a cylindrical Gaussian surface zero?

The magnetic field vector is always tangent to the lateral surface of the cylinder, and since the magnetic field is parallel to the surface, the dot product of the magnetic field vector and the surface area vector is zero. Thus, the flux through the lateral surface is zero.

Why is the magnetic flux through the bases of the cylindrical Gaussian surface zero?

The magnetic field vector lies in the plane of the base of the cylinder and is perpendicular to the surface area vector of the base. Therefore, the dot product of the magnetic field vector and the surface area vector is zero, resulting in zero magnetic flux through both bases.