Which of the following is NOT true according to Faraday's experiments? 

Explanation:

Faraday's Experiments on Electromagnetic Induction

Definition: Michael Faraday conducted a series of experiments in the early 19th century that led to the discovery of electromagnetic induction, which is the process of generating an electromotive force (emf) or voltage across an electrical conductor in a changing magnetic field.

Working Principle: Faraday's experiments demonstrated that an emf could be induced in a conductor when it is exposed to a changing magnetic field. This phenomenon is described by Faraday's Law of Induction, which states that the induced emf in a closed circuit is equal to the negative rate of change of the magnetic flux through the circuit.

Faraday's Law of Induction:

• Mathematically, Faraday's Law is expressed as:
  \(\mathcal{E} = -N \frac{d\Phi}{dt}\)
  where:
  \(\mathcal{E}\) = Induced electromotive force (emf)
  \(N\) = Number of turns in the coil
  \(\Phi\) = Magnetic flux through the coil
  \(\frac{d\Phi}{dt}\) = Rate of change of magnetic flux

Correct Option Analysis:

The correct option is:

Option 1: A static magnetic field produces a current flow in a closed circuit.

This option is NOT true according to Faraday's experiments. Faraday's experiments showed that a current is induced in a closed circuit only when there is a change in the magnetic field. A static (unchanging) magnetic field does not produce a current flow in a closed circuit. This is because a static magnetic field does not induce an emf, and therefore, no current is generated.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: Induced electromotive force = \(\rm -N \frac{d\psi}{dt}\)

This option is true. The expression \(\rm -N \frac{d\psi}{dt}\) is a representation of Faraday's Law of Induction, where \(\psi\) (psi) represents the magnetic flux (\(\Phi\)). This equation correctly describes the relationship between the induced emf and the rate of change of magnetic flux.

Option 3: Induced electromotive force = \(\rm -\frac{d\lambda }{dt}\)

This option is also true. The expression \(\rm -\frac{d\lambda }{dt}\) can be interpreted as a specific case of Faraday's Law of Induction, where \(\lambda\) (lambda) represents the magnetic flux linkage. This equation is consistent with Faraday's law when considering a single loop (N=1).

Option 4: A time-varying field produces an induced voltage in a closed circuit.

This option is true. Faraday's experiments clearly demonstrated that a time-varying (changing) magnetic field induces a voltage (emf) in a closed circuit. This is the fundamental principle behind electromagnetic induction and the operation of devices like transformers and electric generators.

Conclusion:

Faraday's experiments on electromagnetic induction were groundbreaking and formed the basis for much of modern electrical engineering. Understanding that a static magnetic field does not induce a current, while a changing magnetic field does, is crucial for grasping the principles of electromagnetic induction. Faraday's Law of Induction mathematically describes how the induced emf is related to the rate of change of magnetic flux, and these principles are widely applied in various technologies and applications today.