Question

What is the formula for magnetic field intensity?

Answer 1

Could you specify whether you're looking for the formula in a particular context, like for a straight wire, a solenoid, or another scenario?

Answer 2

Magnetic field intensity, often denoted by \( \mathbf{H} \), is a measure of the strength of the magnetic field generated by currents and magnetic materials. It can be expressed in several contexts, but the general formula for \( \mathbf{H} \) in free space is:

\[ \mathbf{H} = \frac{\mathbf{B}}{\mu_0} \]

where:
- \( \mathbf{H} \) is the magnetic field intensity (measured in amperes per meter, A/m).
- \( \mathbf{B} \) is the magnetic flux density (or magnetic induction) (measured in teslas, T).
- \( \mu_0 \) is the permeability of free space, which has a constant value of approximately \( 4\pi \times 10^{-7} \, \text{H/m} \) (henries per meter).

In more complex scenarios involving materials with different magnetic properties, the relationship between \( \mathbf{B} \) and \( \mathbf{H} \) is:

\[ \mathbf{B} = \mu \mathbf{H} \]

where:
- \( \mu \) is the permeability of the material (measured in henries per meter, H/m).
- \( \mu \) can be expressed as \( \mu = \mu_0 \mu_r \), where \( \mu_r \) is the relative permeability of the material.

Thus, in materials other than free space, the formula for \( \mathbf{H} \) becomes:

\[ \mathbf{H} = \frac{\mathbf{B}}{\mu} \]

Here, \( \mathbf{B} \) is still the magnetic flux density, and \( \mu \) is the material’s permeability.