Question

derive the expression for induced emf​

Answer 1

Explanation: According to Faraday's law, when change in magnetic flux in a conductor then, the emf induced in the conductor that means the current induced in the conductor.

Change in flux = bldx

Where, dx = small distance moved by conductor in the magnetic field

b = magnetic field

l = length of the conductor

Now, the induced emf is  

induced emf = change in flux /change in time

emf = bl\dfrac{dx}{dt}emf=bldtdx​

emf = blvemf=blv

Where, \dfrac{dx}{dt} = vdtdx​=v

Hence, when a conductor of length l is moved with a uniform velocity v normal to a uniform magnetic field b.

Then, the induced emf is

emf = blvemf=blv

Now, the induced current is

Current = emf/ resistance

I = \dfrac{blv}{r}I=rblv​

Hence, This is the required solution.