A wire in the form of a circular loop of radius 10 cm lies in a plane normal to a magnatic field of 100T. if this wire is pulled to take a square shape in the same plane in 0. 1 s. the average induced emf is.?

Question

Answer

Given

Radius of circular loop = 10 cm

Magnetic field = 100 T

Time taken to pull the wire into a square shape = 0.1 s

To Find

Average induced emf

Solution

When the wire is pulled to take a square shape in the same plane, the magnetic flux through the wire changes. This change in magnetic flux induces an emf in the wire, which is given by Faraday's Law of Electromagnetic Induction:

emf = -N(dΦ/dt)

Where N is the number of turns in the wire and dΦ/dt is the rate of change of magnetic flux through the wire. In this case, the wire is a single turn, so N = 1.

The magnetic flux through the circular loop is:

Φ = Bπr^2

Where B is the magnetic field, r is the radius of the loop, and π is pi. Substituting the given values:

Φ = (100 T) x π x (0.1 m)^2 = 0.0314 Wb

When the wire is pulled into a square shape, the magnetic flux through the wire changes. The new magnetic flux through the wire is:

Φ' = B x (2a)^2

Where B is the magnetic field and a is the side of the square. Substituting the given values:

Φ' = (100 T) x (0.2 m)^2 = 0.004 Wb

The rate of change of magnetic flux is:

dΦ/dt = (Φ' - Φ)/t

Substituting the given values:

dΦ/dt = (0.004 Wb - 0.0314 Wb)/(0.1 s) = -0.273 Wb/s

The negative sign indicates that the emf induced in the wire is opposite in direction to the change in magnetic flux. Therefore:

emf = -N(dΦ/dt) = -1 x (-0.273 V) = 0.273 V

Answer

The average induced emf is 0.273 V.

Answer

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