What is the difference between an induced current and a current passing through the coil?

Induced current and current through a coil are two different concepts, each with distinct physical principles and applications. Below is a detailed explanation of the differences between these two types of currents:

1. Induced Current 

Definition:

Induced current is the current generated in a conductor due to the electromagnetic induction effect caused by a changing magnetic field. According to Faraday's law of electromagnetic induction, when the magnetic flux through a closed loop changes, an electromotive force (EMF) is induced in the loop, which in turn generates a current.

Conditions for Generation:

• Changing Magnetic Field: The magnetic field must vary with time, such as by moving a magnet or altering the current.

• Closed Loop: The conductor must form a closed loop to allow current to flow.

Mathematical Expression:

Faraday's law of electromagnetic induction can be expressed as:

where 

E is the induced EMF, ΦB is the magnetic flux, and t is time.

Applications:

• Generators: Utilize the change in magnetic field to generate induced current, converting mechanical energy into electrical energy.

• Transformers: The alternating current in the primary coil creates a changing magnetic field, which induces current in the secondary coil to transfer electrical energy.

• Induction Heating: Uses a changing magnetic field to induce eddy currents in metals, achieving heating effects.

2. Current Through the Coil 

Definition:

Current through the coil is the current that directly flows through the conductors of the coil. This current can be either a constant direct current (DC) or an alternating current (AC).

Conditions for Generation:

• Power Source: An external power source (such as a battery, generator, or AC source) is required to provide the current.

• Closed Loop: The coil must be part of a closed circuit to allow current to flow.

Mathematical Expression:

For direct current (DC), Ohm's law can be used:

where I is the current, V is the voltage, and R is the resistance.

For alternating current (AC), the current can be expressed as a sine wave:

where I0 is the maximum current, ω is the angular frequency, and ϕ is the phase angle.

Applications:

• Electromagnets: The current through the coil generates a magnetic field, used to create electromagnets.

• Motors: The alternating current through the coil generates a rotating magnetic field, driving the motor.

• Transformers: The alternating current in the primary coil creates a changing magnetic field, which induces current in the secondary coil to transfer electrical energy.

Summary

• Induced Current is the current generated in a conductor due to the electromagnetic induction effect caused by a changing magnetic field, requiring a changing magnetic field and a closed loop.

• Current Through the Coil is the current that directly flows through the conductors of the coil, requiring an external power source and a closed circuit.

Understanding the differences between these two types of currents helps in better grasping the fundamental principles of electromagnetism and correctly selecting and using related technologies in practical applications.