The following shows a semicircle of length L, moving with velocity v in a uniform magnetic field.
The expression for the induced emf in a conductor of length l is given by,
The expression for the induced emf in a conductor of length
l is
given by
e‌‌=B(v×I) ‌‌=Bvl‌sin‌θ‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I) The effective length of arc for induced emf is given by,
l‌eff ‌=2R =‌‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(II) From equations (1) and (2)
e=Bv‌‌sin‌45∘(∵θ=45∘) e=BvL‌‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(III) The induced emf is given by,
φ=αBvL‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(IV) Therefore, from equations (3) and (4)
α=‌