Magnetic Excitation Formula Explanation

This question asks about the magnetic excitation inside a magnetic core that is wound with a circular coil. Magnetic excitation is essentially the measure of the magnetic field intensity generated by the current flowing through the coil windings.

Understanding Magnetic Excitation

In electromagnetism, the magnetic field intensity, often referred to as magnetic excitation, quantifies the influence of magnetic poles on a point in space. For a coil carrying current, the magnetic excitation depends on the number of turns in the coil, the current passing through it, and the geometry of the coil, specifically its length or the path length around the core.

Deriving the Formula

The magnetomotive force (MMF) is the driving force behind the magnetic field in a magnetic circuit. It is calculated as the product of the number of turns ($n$) and the current ($I$) flowing through the coil:

$$MMF = nI$$

Magnetic excitation ($H$), also known as magnetic field intensity, is defined as the MMF per unit length of the magnetic path. Assuming the magnetic core forms a path of length $L$ (like a solenoid or a toroid), the magnetic excitation inside the core is given by:

$$H = \frac{MMF}{L}$$

Substituting the expression for MMF:

$$H = \frac{nI}{L}$$

Applying to the Given Problem

In this specific problem:

• The coil has $n$ turns.
• The current passing through the coil is $I$.
• The length associated with the magnetic core path is $L$.

Therefore, the magnetic excitation inside the core is calculated using the formula derived above:

$$H = \frac{nI}{L}$$

This matches the first option provided.

Conclusion

The magnetic excitation inside the core is determined by the total MMF ($nI$) distributed over the length ($L$) of the magnetic path. The correct formula representing this relationship is $\frac{nI}{L}$.