What is the formula for the induced current?

Understanding Induced Current and Its Formula

Introduction

Electromagnetic induction is a fascinating phenomenon that occurs when a conductor is exposed to a changing magnetic field, resulting in the generation of an electric current. This current, known as induced current, plays a crucial role in various electrical and electronic applications.

Faraday’s Law of Electromagnetic Induction

The fundamental principle that governs electromagnetic induction is Faraday’s law. This law states that the electromotive force (EMF), or induced voltage (ε), generated in a conductor is directly proportional to the negative rate of change of magnetic flux (Φ_B) through the conductor:

ε = -dΦ_B/dt

where:

• ε is the induced voltage in volts (V)
• Φ_B is the magnetic flux in webers (Wb)
• t is time in seconds (s)

Lenz’s Law

Lenz’s law, an extension of Faraday’s law, provides a qualitative understanding of the direction of induced current. According to Lenz’s law, the direction of the induced current is such that it opposes the change in magnetic flux that produced it.

Formula for Induced Current

The formula for induced current (I) can be obtained by combining Faraday’s law with Ohm’s law, which relates voltage (ε), current (I), and resistance (R):

ε = IR

Substituting the Faraday’s law equation for ε, we get:

-dΦ_B/dt = IR

Assuming constant resistance, we can solve for induced current:

I = -dΦ_B/Rdt

Conclusion

The formula for induced current, I = -dΦ_B/Rdt, provides a quantitative understanding of the relationship between changing magnetic flux, conductor resistance, and the resulting current. This knowledge is essential in designing electrical devices, such as transformers, generators, and motors, where manipulation of induced currents is crucial for efficient operation.