What Is Faraday's Law?
Faraday's law of electromagnetic induction states that a changing magnetic flux through a coil induces an electromotive force (EMF). The magnitude of that EMF is proportional to the number of wire turns and how quickly the flux changes. This calculator finds the induced EMF directly from the coil turns, the change in magnetic flux, and the time over which the change occurs.
How to Use This Calculator
Enter the number of turns (\(N\)) in the coil, the change in magnetic flux \(\Delta\Phi\) in webers (Wb), and the change in time \(\Delta t\) in seconds. The calculator returns the induced EMF in volts. The negative sign (Lenz's law) indicates that the induced EMF opposes the change in flux; the magnitude row shows the absolute value.
The Formula Explained
The equation is $$\varepsilon = -\,N \cdot \frac{\Delta\Phi}{\Delta t}$$ where \(N\) is the number of turns, \(\Delta\Phi\) is the change in magnetic flux in webers, and \(\Delta t\) is the elapsed time in seconds. Magnetic flux \(\Phi\) equals the magnetic field \(B\) multiplied by the area \(A\) it passes through (\(\Phi = B \cdot A\)). The faster the flux changes or the more turns present, the larger the induced voltage.
Worked Example
A coil with 100 turns experiences a flux change of 0.05 Wb over 0.1 seconds. $$\varepsilon = -100 \times \frac{0.05}{0.1} = -50 \text{ V}$$ The magnitude of the induced EMF is 50 volts.
FAQ
Why is the EMF negative? The minus sign reflects Lenz's law: the induced current flows in a direction that opposes the change in magnetic flux that produced it.
What is a weber? A weber (Wb) is the SI unit of magnetic flux, equal to one volt-second. One weber per square meter equals one tesla.
How can I increase the induced EMF? Increase the number of turns, increase the rate of flux change (stronger field or faster motion), or reduce the time over which the change happens.
