Why is a magnetic field outside the toroid zero ?

The magnetic field outside a toroid is typically zero due to the nature of the magnetic flux lines within the toroid core. A toroid is a ring-shaped core typically made of ferromagnetic material around which a coil is wound. When current flows through the coil, it generates a magnetic field. In a toroid, this magnetic field is confined largely within the core due to the continuous loop of the core material. The magnetic flux lines inside the toroid core follow a closed path around the core, resulting in negligible external magnetic field outside the toroid. This containment of magnetic flux lines within the core effectively results in a near-zero magnetic field outside the toroid.

Similarly, the magnetic field outside a coil is zero in ideal conditions because the magnetic field generated by the current-carrying coil is predominantly confined within the coil itself. When an electric current passes through a coil, it generates a magnetic field that forms concentric circles around the coil according to Ampère’s law. However, at a significant distance away from the coil, the magnetic field strength diminishes rapidly and approaches zero. This phenomenon is due to the magnetic flux lines closing within the coil’s surrounding space, resulting in minimal magnetic field outside the coil.

A toroid is a geometric shape resembling a doughnut or ring, typically made of a material with high magnetic permeability such as iron. It is used in electrical transformers, inductors, and other magnetic devices due to its ability to efficiently confine magnetic flux within its circular core. The magnetic field outside a toroid is generally very weak or zero because the magnetic flux lines generated by the current in the coil windings are tightly confined within the core material. This confinement ensures that there is little to no magnetic field extending beyond the toroid’s outer surface, making it useful for applications where magnetic shielding or concentration is required.

The magnetic field inside a toroid is not zero and is concentrated within the core material due to the circular path taken by the magnetic flux lines. The winding of the coil around the toroid creates a magnetic field that circulates around the core. Inside the toroid, the magnetic field is uniformly distributed along the core’s cross-sectional area, providing efficient magnetic coupling for transformers and inductors.

The magnetic field at the center of a toroid is generally zero due to the symmetry of the toroidal geometry and the cancellation of magnetic field components from all sides. At the center of the toroid, the magnetic fields generated by each segment of the coil windings around the core tend to cancel each other out. This results in a net magnetic field strength of zero at the geometric center of the toroid, where the contributions from all sides of the toroidal core nullify each other. Thus, the magnetic field is effectively zero at the center of the toroid, contributing to its unique magnetic field characteristics and applications in magnetic devices.

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