# How to calculate magnetic flux from voltage?

## Main Question or Discussion Point

I understand that magnetic flux density is measured in Teslas or Weber’s per square meter and that voltage or emf is measured using faraday’s law of induction which is
E= - N dφ/dt
Where
N= number parallel fields
Φ = magnetic flux (Wb)
E= emf (V)
What I don’t understand is the time function of the formula. If we rearranged the formula to make flux the subject what would the time function represent? Correct me if I’m wrong but If there is constant voltage and current through a coil then there is a constant magnetic field inside the coil (or through the core if there is one).

In this situation, what does the time variable represent?

Related Electrical Engineering News on Phys.org
anorlunda
Staff Emeritus
If there is constant voltage and current through a coil then there is a constant magnetic field inside the coil
You are confused because of the contradiction in your sentence. If the current in an ideal coil is steady, there is a constant field, and there is no voltage. The voltage across a coil is proportional to the rate of change of current. That is where time comes in.

Thank you for clarifying that.
So if there is no rate of change in current there is no voltage.

Tom.G
I understand that magnetic flux density is measured in Teslas or Weber’s per square meter and that voltage or emf is measured using faraday’s law of induction which is
E= - N dφ/dt
Where
N= number parallel fields
Φ = magnetic flux (Wb)
E= emf (V)
What I don’t understand is the time function of the formula. If we rearranged the formula to make flux the subject what would the time function represent? Correct me if I’m wrong but If there is constant voltage and current through a coil then there is a constant magnetic field inside the coil (or through the core if there is one).

In this situation, what does the time variable represent?
The formula you gave works to find the voltage generated in a coil when their is a magnetic field affecting the coil. If you have a permanent magnet and a coil of wire on a table next to each other and not moving, then there is no voltage induced in the coil. Now if you move one of them there is a voltage induced in the coil - the faster you move them in relation to each other the higher the voltage. That is the time term, dt, in the formula. Also, the more the magnetic field changes, dφ, the higher the voltage.

There is a simulation of this at: https://micro.magnet.fsu.edu/electromag/java/faraday2/

For the second part of your understanding, when a wire, or a coil, has current flowing thru it there is a magnetic field generated. Which end is North or South depends on which direction the current is flowing. If there is AC flowing, the field varies with the AC. In either case, AC or DC, the strength of the field is determined by the amount of current, the number of coil turns, and if there is a core, what material is used for a core.

Cheers,
Tom

The formula you gave works to find the voltage generated in a coil when their is a magnetic field affecting the coil. If you have a permanent magnet and a coil of wire on a table next to each other and not moving, then there is no voltage induced in the coil. Now if you move one of them there is a voltage induced in the coil - the faster you move them in relation to each other the higher the voltage. That is the time term, dt, in the formula. Also, the more the magnetic field changes, dφ, the higher the voltage.

There is a simulation of this at: https://micro.magnet.fsu.edu/electromag/java/faraday2/

For the second part of your understanding, when a wire, or a coil, has current flowing thru it there is a magnetic field generated. Which end is North or South depends on which direction the current is flowing. If there is AC flowing, the field varies with the AC. In either case, AC or DC, the strength of the field is determined by the amount of current, the number of coil turns, and if there is a core, what material is used for a core.

Cheers,
Tom
Thank you, I found the simulation helpful.

Tom.G