The Induced EMF in a Rotating Copper Rod

When a copper rod of length l is rotating about its midpoint perpendicular to a magnetic field B with a constant angular velocity ω, an electromotive force (EMF) is induced between the two ends of the rod. This phenomenon is known as electromagnetic induction.

Explanation:

To understand the phenomenon of induced EMF in a rotating copper rod, let's break down the explanation into several key points:

Fleming's Right-hand Rule:
According to Fleming's right-hand rule, when a conductor moves in a magnetic field, an induced current is produced in the conductor. The direction of this induced current can be determined using the right-hand rule.

Magnetic Field and Magnetic Flux:
When the copper rod rotates about its midpoint, it cuts through the magnetic field lines present in the region. This cutting of magnetic field lines results in the change of magnetic flux through the rod.

Faraday's Law of Electromagnetic Induction:
According to Faraday's law of electromagnetic induction, the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux through a conductor.

Induced EMF Calculation:
The induced EMF can be calculated using the formula:
EMF = -N * (ΔΦ/Δt)
where EMF is the induced electromotive force, N is the number of turns in the coil, ΔΦ is the change in magnetic flux, and Δt is the time taken for the change to occur.

Angular Velocity and Magnetic Flux:
In the given scenario, the copper rod is rotating with a constant angular velocity ω. As the rod rotates, the angle between the magnetic field lines and the rod changes. This change in angle leads to a change in the magnetic flux through the rod.

Direction of Induced Current:
Using Fleming's right-hand rule, we can determine the direction of the induced current. The direction of the magnetic field, the direction of the rotational motion, and the direction of the induced current form a right-hand system.

Summary:
In summary, when a copper rod of length l rotates about its midpoint perpendicular to a magnetic field B with a constant angular velocity ω, an induced EMF is generated between the two ends of the rod. This phenomenon is a result of electromagnetic induction, which occurs due to the change in magnetic flux through the rotating rod. The magnitude and direction of the induced EMF can be determined using Faraday's law of electromagnetic induction and Fleming's right-hand rule, respectively.