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Question
How will you induce an emf by changing the area enclosed by the coil?
Solution
Consider a conducting rod of length 1 moving with a velocity v towards left on a rectangular metallic framework. The whole arrangement is placed in a uniform magnetic field `vec"B"` whose magnetic lines are perpendicularly directed into the plane of the paper. As the rod moves from AB to DC in a time dt, the area enclosed by the loop and hence the magnetic flux through the loop decreases.
× → `vec"B"` (⊥r, inwards)
Production of induced emf by changing the area enclosed by the loop
The change in magnetic flux in time dt is
dΦB = B x change in area
B x Area ABCD
= Blvdt since Area ABCD = l(vdt)
or `("d"Φ_"B")/"dt"` = Blv
As a result of a change in flux, an emf is generated in the loop. The magnitude of the induced emf is
ε = `("d"Φ_"B")/"dt"` = Blv
This emf is called motional emf. The direction of induced current is found to be clockwise from Fleming’s right-hand rule.
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