State whether emf induced in followling cases

1 A conductor of length l falling freely in NS direction

2 A conductor of length l falling freely in EW direction

To determine whether an electromotive force (emf) is induced in the two scenarios you mentioned, we need to consider the principles of electromagnetic induction, particularly Faraday's law. This law states that a change in magnetic flux through a circuit induces an emf in that circuit. The direction of the induced emf can be understood through the right-hand rule and the orientation of the magnetic field.

Scenario 1: Conductor Falling Freely in the NS Direction

In this case, if a conductor of length l is falling freely in the north-south (NS) direction, we need to consider the Earth's magnetic field, which generally runs from the magnetic south to the magnetic north. As the conductor falls, it cuts through the magnetic field lines. The key point here is that the motion of the conductor relative to the magnetic field will induce an emf.

• The conductor is moving downward, cutting through the magnetic field lines.
• This motion results in a change in magnetic flux through the area enclosed by the conductor.

Thus, an emf is indeed induced in the conductor as it falls in the NS direction. The direction of the induced current can be determined using the right-hand rule, where the thumb points in the direction of the conductor's motion (downward), and the fingers point in the direction of the magnetic field (from south to north). The palm will then face the direction of the induced current.

Scenario 2: Conductor Falling Freely in the EW Direction

Now, let’s analyze the second scenario where the conductor is falling freely in the east-west (EW) direction. Similar to the first case, we must consider the orientation of the Earth's magnetic field. In this case, the magnetic field lines still run from south to north, but the conductor is moving horizontally.

• The conductor is moving perpendicular to the direction of the magnetic field lines.
• Since it is not cutting through the magnetic field lines in a vertical manner, there is no change in magnetic flux through the area enclosed by the conductor.

As a result, no emf is induced in the conductor falling in the EW direction. The motion does not create a change in magnetic flux, which is essential for inducing an emf according to Faraday's law.

Summary of Findings

To summarize:

• In the NS direction, an emf is induced due to the conductor cutting through the magnetic field lines.
• In the EW direction, no emf is induced as the conductor does not change the magnetic flux through its area.

Understanding these principles helps clarify how motion and magnetic fields interact to produce electrical energy, which is foundational in electromagnetism and its applications in technology.