The magnetic field outside a toroidal coil:

Explanation:

The magnetic field outside a toroidal coil is zero. Let's delve into the detailed explanation and reasoning behind this conclusion.

Understanding the Toroidal Coil:

A toroidal coil, or simply a toroid, is a coil of wire in the shape of a doughnut or a closed loop. The wire is wound around a circular core, and the core itself can be either solid or hollow. The purpose of this design is to confine the magnetic field within the core and minimize the magnetic field outside the coil.

Magnetic Field in a Toroidal Coil:

To understand why the magnetic field outside a toroidal coil is zero, we need to consider the principles of electromagnetism, specifically Ampère's Law. Ampère's Law states that the line integral of the magnetic field B around any closed loop is proportional to the total current I passing through the loop. Mathematically, it is expressed as:

B × dl = μ₀ × I

where:

• B is the magnetic field
• dl is a differential element of the loop
• μ₀ is the permeability of free space
• I is the current passing through the loop

In the case of a toroidal coil, the wire is wound in such a way that the current flows in circular loops around the core. Because the coil is wound symmetrically and continuously around the core, the magnetic field inside the core is also circular and confined within the core. The magnetic field lines inside the toroid follow the loops of the wire, creating a strong and uniform magnetic field within the core.

Why the Magnetic Field Outside is Zero:

Outside the toroidal coil, the contributions of the magnetic field from each loop of the wire cancel each other out. This is due to the symmetry and closed-loop nature of the toroid. For any point outside the toroid, there are equal and opposite magnetic field contributions from different sections of the coil, resulting in a net magnetic field of zero.

Mathematically, this can be understood by applying Ampère's Law to a closed loop that lies outside the toroid. Since no net current passes through this loop (the current entering the loop at one point is exactly balanced by the current leaving the loop at another point), the line integral of the magnetic field around this loop is zero. Consequently, the magnetic field outside the toroid must be zero to satisfy Ampère's Law.

Therefore, the correct option is:

1) The magnetic field outside a toroidal coil is zero.