Question

The tightly wound toroidal solenoid is one of the few configurations for which it is easy to calculate self-inductance. What features of the toroidal solenoid give it this simplicity?

Short answer

Answer

Toroidal solenoid has geometric configuration

Step-by-step solution

Definition of solenoid

The term solenoid may be defined as the cylindrical coil of wire acting as a magnet when flowing carrying electric current through it.

Determine the feature of the toroidal solenoid give it this simplicity

If assume that magnitude over the entire cross section area then

$$\begin{gathered} {\varphi }_B=B.A \\ {\varphi }_B=\frac{{\mu }_0{N}_{i}A}{2\pi r} \end{gathered}$$

If the flux through each turn same then

$$\begin{gathered} L=\frac{N{\varphi }_B}{2\pi r} \\ L=\frac{{\mu }_0{N}^{2}A}{2\pi r} \end{gathered}$$

Hence, Toroidal solenoid has geometric configuration.