A metallic ring of radius R moves in a vertical plane in the presence of a uniform magnetic field B ⊥ to the plane of ring. At any given instant of time, its centre of mass moves with a velocity v while ring rotates in its COM frame with angular velocity ω. The magnitude of induced EMF between pts O & P is?

Dear student,
Assumptions:

The direction of rotation of the ring: Counterclockwise direction
The direction of motion of electrons in the ring: Along positive y-direction
The direction of magnetic field: z-direction
Lorentz's law:

F=-e v × B   =-e v j × B k^   = -evB  j ×  k^    = -evB  i      =-evBi

From the above expression, it is clear that the direction of the force of electrons is in the direction of the negative x-axis.

Reason for induced emf:

Current is caused by the movement of electrons towards the centre. This will produce emf in
the ring between the point O and P.

The expression of induced emf:

ε = dϕdt   =ddtBA   =B ddt12πr2θ  =12πr2Bdθdt  =12πr2Bω  =12πr2B2πν  =π2r2Bν
Regards

  • -16
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