A rectangular, a square, a circular and an elliptical loop, all in the x-y plane, are moving out of a uniform magnetic field with a constant velocity ⃗v=v̂i. The magnetic field is directed along the negative z direction. The induced emf, during the passage of these loops out of the field region, wi…

Question

A rectangular, a square, a circular and an elliptical loop, all in the x-y plane, are moving out of a uniform magnetic field with a constant velocity ⃗v=v̂i. The magnetic field is directed along the negative z direction. The induced emf, during the passage of these loops out of the field region, will NOT remain constant for

Accepted Answer

(1) the circular and the elliptical loops. The emf is Bℓ v, where ℓ is the length of the boundary that lies along the edge of the field region at that instant. A rectangle or a square leaving edge-on presents a whole side of fixed length, so ℓ does not change and the emf stays constant throughout the passage. For a circle or an ellipse the chord at the field boundary starts small, grows to a maximum and shrinks again, so ℓ changes continuously and the emf changes with it. So the emf fails to remain constant for exactly the circular and elliptical loops.

Step-by-step solution

Why the other options are wrong