Figure 29-72 shows an arrangement known as a Helmholtz coil....

Figure $29-72$ shows an arrangement known as a Helmholtz coil. It consists of two circular coaxial coils, each of 200 turns and radius $R=25.0 \mathrm{~cm},$ separated by a distance $s=R .$ The two coils carry equal currents $i=12.2 \mathrm{~mA}$ in the same direction. Find the magnitude of the net magnetic field at $P$, midway between the coils.

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Key Concepts

Helmholtz Coil

A Helmholtz coil is a specific arrangement of two identical circular coils that are parallel and coaxial, separated by a distance typically equal to the radius of the coils. This setup is used to produce a region of nearly uniform magnetic field in the central area between the coils. The uniformity of the magnetic field is critical in experiments and applications where consistency and precision are required.

Magnetic Field of a Circular Current Loop

The magnetic field produced by a circular loop of current can be calculated using the Biot–Savart law, which relates the magnetic field to the current and the geometry of the current path. Along the axis of the loop, the field has a specific analytic form, and this principle is used to determine the contribution of each coil to the total magnetic field in arrangements like the Helmholtz coil.

Superposition Principle in Magnetostatics

In magnetostatics, the superposition principle states that the magnetic field generated by multiple sources is the vector sum of the fields produced by each individual source. This principle allows for the calculation of the net magnetic field at a specific point by adding the fields due to each coil, which is essential in analyzing configurations like the Helmholtz coil setup.

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