Question

Derive an expression for induced emf in rectangular coil moving perpendicular to uniform magnetic field with uniform velocity. Draw necessary diagram.​

Answer 1

Explanation:

U-shaped conductor abcd lying normal to a uniform magnetic field B⃗ B→. Let a conductor rod PQ is placed on frame abed and let it be moving with a uniform velocity v⃗ v→. As the rod moves by a small distance dx = v dt, the area enclosed changes from QcbP to Qʻcbp.

Thus, change in magnetic flux

dfB=B(dA)=B[areaQcbP→Q.cbP.]dfB=B(dA)=B[areaQcbP→Q.cbP.]

= B (area Q.QPP.) = B l dx = B lvdt

∴∴ magnitude for induced emf |ɛ|=dϕBdt=Blvdtdt=Blv|ɛ|=dϕBdt=Blvdtdt=Blv

If R be the resistang of the loop then induced current |I|=|ɛ|R=BlvR.