Question

Write the statement of Lenz's law of electromagnetic induction.
A $2$ m horizontal long straight conducting wire extending from east to west direction is falling with a speed of $5$m/s perpendicular to the horizontal component of the earth's magnetic field \[0.3 \times {10^{ - 4}}\] tesla. Calculate the value of instantaneous emf induced across the ends of wire.

Answer 1

Hint: This is a question related to the topic electromagnetic induction. The Lenz’s law is related to the polarity of the induced emf when there is condition like production of the emf when there is a change in the magnetic field surrounding their region.

Complete answer:
Statement of the Lenz’s law: Lenz’s law states that when an emf is produced due to a change in the existing magnetic flux (according to Faraday’s law), then polarity of the induced emf will be such that it will produce an induced current that’s magnetic field opposes the change which produces it.

That means the induced current will oppose the change in the magnetic flux (due to which the induced current is getting generated).
In the numerical part we have given,
Length of the conductor= $l = 2m$
Speed of the conductor in the magnetic field=$v = 5$m/s
Value of the magnetic field which is the horizontal value of the earth magnetic field= $B = 0.3 \times {10^{ - 4}}$ tesla.

As we all know the formula for the emf induced across the ends of wire. When a conductor is moving in a magnetic field with some velocity.
So here, emf induced across the ends of wire =$E = Bvl$------equation (1)
Now pouting all the values from given, we get
$E = (0.3 \times {10^{ - 4}} \times 5 \times 2)$
$ \Rightarrow E = 3 \times {10^{ - 4}}V$

Hence, the value of instantaneous emf induced across the ends of wire is $3 \times {10^{ - 4}}V$.

Note:
Faraday's law also tells us that the emf can be induced in a conductor either by passing the conductor through a magnetic field or by moving the magnetic field past the conductor and if the conductor will be a part of a closed electrical circuit then the current will flow through the conductor. The emf induced by the relative motion of the conductor is known as motional emf.