When a small magnet is moved into or out of a solenoid an emf is induced in the coil. However, if the magnet is moved into or out of the center of a toroidal coil (picture a donut with the magnet moving into and out of the
Explanation : Toroid is nothing but endless solenoid.
To induce emf there must be chage in the magnetic flux through the toroid,this change in magnetic flux is taken place by chagning magnetic filed lines through the toroid,or chagnging the area exposed to magnetic filed or chagning the orientation of filed.
Here in this problem we are simly moving the magnet into or out of the center of the toroidal coil which does not changes the magnetic flux through the toroid
So there is no induce emf in the toroid
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