A toroidal inductor with an inductance of 90.0 mH encloses a volume of 0.020 m^3 . If the averag

step 1 So we know that the magnetic energy stored in a toroid would be equal to one half times the torr

A toroidal inductor with an inductance of 90.0 mH encloses a...

A toroidal inductor with an inductance of 90.0 $\mathrm{mH}$ encloses
a volume of 0.020 $\mathrm{m}^{3} .$ If the average energy density in the toroid is
$70.0 \mathrm{J} / \mathrm{m}^{3},$ what is the current through the inductor?

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Key Concepts

Energy Density

Energy density refers to the amount of energy stored per unit volume. In systems where energy is distributed over a spatial extent, such as the magnetic field in a toroidal inductor, the total energy can be calculated by multiplying the average energy density by the volume in which the energy is stored.

Magnetic Energy Storage

Magnetic energy storage in an inductor is the concept that the energy stored in the magnetic field of an inductor is given by the expression (1/2) L I², where L is the inductance and I is the current. This relationship is fundamental in circuits using inductive elements, allowing one to connect the inductor’s physical properties (through L) with the current flowing through it.

Inductance

Inductance is a measure of how effectively an inductor converts current into magnetic energy. It depends on the geometry of the coil and the magnetic properties of the core material, and it plays a key role in determining how much magnetic energy is stored for a given current, as shown by the formula for magnetic energy storage in an inductor.

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