1 Answer
The formula for Electromotive Force (EMF) or Electromagnetic Induction (EMI) is derived from Faraday's Law of Induction. It describes how a changing magnetic field can induce an electric current (EMF) in a conductor.
The formula is:
\[
\mathcal{E} = - \frac{d\Phi_B}{dt}
\]
Where:
The negative sign in the equation is due to Lenz's Law, which indicates that the direction of the induced EMF opposes the change in the magnetic flux that caused it.
If you are dealing with a coil of wire, the induced EMF can also be expressed as:
\[
\mathcal{E} = - N \frac{d\Phi_B}{dt}
\]
Where:
This shows that the EMF is proportional to the number of turns in the coil, as each turn contributes to the total induced EMF.
In simple terms, whenever there is a change in the magnetic field (whether by moving a magnet, changing the field strength, or moving a coil), it induces an electric current in a conductor, and this is quantified by the EMF formula.
The formula is:
\[
\mathcal{E} = - \frac{d\Phi_B}{dt}
\]
Where:
- \( \mathcal{E} \) is the induced EMF (volts).
- \( \Phi_B \) is the magnetic flux, which is the product of the magnetic field (\(B\)) and the area (\(A\)) through which the magnetic field is passing, i.e., \( \Phi_B = B \cdot A \cdot \cos(\theta) \), where \( \theta \) is the angle between the magnetic field and the normal to the surface.
- \( \frac{d\Phi_B}{dt} \) is the rate of change of magnetic flux with respect to time.
The negative sign in the equation is due to Lenz's Law, which indicates that the direction of the induced EMF opposes the change in the magnetic flux that caused it.
If you are dealing with a coil of wire, the induced EMF can also be expressed as:
\[
\mathcal{E} = - N \frac{d\Phi_B}{dt}
\]
Where:
- \( N \) is the number of turns in the coil.
This shows that the EMF is proportional to the number of turns in the coil, as each turn contributes to the total induced EMF.
In simple terms, whenever there is a change in the magnetic field (whether by moving a magnet, changing the field strength, or moving a coil), it induces an electric current in a conductor, and this is quantified by the EMF formula.