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Q)

A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. The can be cause
(a) The magnetic field is constant
(b) The magnetic field is in the same plane as the circular coil and it may or may not vary
(c) The magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably.
(d) There is constant magnetic field in the perpendicular (to the plane of the coil) direction

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A)
When a circular coil expands radially in a region of magnetic field, induced $emf$ developed is
$\begin{align*}\; \; \; \; \; \; e& =Blv \\ & = B \times rate\; of\; charge\; of\; area \end{align*}$
It is given that the magnetic field B is in a plane perpendicular to the plane of the circular coil. Since e=0, magnetic field should be in the plane of circular coil so that its component which perpendicular to plane of coil is zero. If the magnetic of the magnetic field decrease with the magnetic flux linked with the coil, then $e = \frac{d \phi}{dt}$= 0
Hence the option b and c.
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