A rectangular, a square, a circular and an elliptical loop, all in the $(x-y)$ plane, are moving out of a unif

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, $\vec{v} = v\hat{i}$. The magnetic field is directed along the negative $z$-axis direction. The induced emf, during the passage of these loops, out of the field region, will not remain constant for:

Accepted Answer

The induced emf is given by $\varepsilon = Blv$, where $B$ is the magnetic field, $v$ is the velocity, and $l$ 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' $l$ (the side perpendicular to velocity) remains constant. Thus, the induced emf $\varepsilon = Blv$ remains constant until the loop is completely out of the field.
2.  **Circular and Elliptical Loops:** As these loops move out, the 'effective length' $l$ (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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