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NEET PHYSICSMedium

A rectangular, a square, a circular and an elliptical loop, all in the (x−y)(x-y) plane, are moving out of a uniform magnetic field with a constant velocity, v⃗=vi^\vec{v} = v\hat{i}. The magnetic field is directed along the negative zz-axis direction. The induced emf, during the passage of these loops, out of the field region, will not remain constant for:

A

the rectangular, circular and elliptical loops

B

the circular and the elliptical loops

C

only the elliptical loop

D

any of the four loops

Step-by-Step Solution

The induced emf is given by ε=Blv\varepsilon = Blv, where BB is the magnetic field, vv is the velocity, and ll is the effective length of the conductor cutting the magnetic field lines perpendicular to the velocity .

  1. Rectangular and Square Loops: As these loops move out of the field with constant velocity along the x-axis, the 'effective length' ll (the side perpendicular to velocity) remains constant. Thus, the induced emf ε=Blv\varepsilon = Blv remains constant until the loop is completely out of the field.
  2. Circular and Elliptical Loops: As these loops move out, the 'effective length' ll (the chord length cutting the field boundary) changes continuously with time. Therefore, the induced emf varies with time and does not remain constant.
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