# Why can we say $F=\phi R=NI=HL$ according to $V=IR$?

"Magnetomotive force is a quantity appearing in the equation for the magnetic flux in a magnetic circuit". This is the explanation of magnetomotive force from Wikipedia. Its equation is:

$$F=\phi R$$ $$\\phi\$$ is the magnetic flux.
$$\R\$$ is the reluctance of the circuit.

Why can we write $$\F=\phi R\$$ from this explanation, that is, "Magnetomotive force is a quantity appearing in the equation for the magnetic flux in a magnetic circuit"? The explanation does't mention $$\R\$$.

Next, Wikipedia says: "It can be seen that the magnetomotive force plays a role in this equation analogous to the voltage V in Ohm's law: V = IR", so, $$F=NI\\F=HL$$ $$\N\$$ is the number of turns in the coil.
$$\I\$$ is the electric current through the coil.
$$\H\$$ is the magnetizing force (the strength of the magnetizing field).
$$\L\$$ is the mean length of a solenoid or the circumference of a toroid.

Why can we write $$\F=NI=HL\$$ according to Ohm's law: $$\V=IR\$$ ?

Can anyone tell me the answers to these two questions ?

• You can't literally say F=NI=HL implies V=IR. I believe it's just meant to be an analogy. In the magnetic version of the equations flux is similar to current. Mar 15, 2022 at 8:17

## 1 Answer

As user4574 mentioned in their comment, I think you are confusing Hopkinson's law with Ohm's law, because both are analogous. The R in F=ϕR is not for resistance, but for reluctance, which, following the electrical analogy, is the "resistance" to the circulation of magnetic flux, that would be analogous to the electrical current. You can read more here: Resistance–reluctance model

About your second question, and extending from the prior answer, F=NI=HL has nothing to do with V=IR further than the similarity of both equations.