Electromagnetic induction and alternating current | Learn Physics

Example of electromagnetic induction and alternating current

Example:  a magnetic field induction is changing in magnitude at a constant rate dB/dt. A given mass m of copper drawn into a wire of radius a and formed into a loop of radius r is placed perpendicular to the field. Shows that the induced current in the loop is given I = (m/4πρ∂)dB/dt

Where ρ is specific resistance and ∂ is density of copper.

Solution:

Area of loop = πr²

Area of cross section = πa²

Mass of wire, m = (πa²) l ×∂           ……………….(i)

Resistance of wire R = ρl/ πa²

Using (i) ,        R = ρl/(m/l∂) = ρl²∂/m

   R= [ρ(2πr)² ∂/m = 4π²r²∂ρ/m    …………………(ii)

Flux through the loop ɸ = BA = B (πr²)

E = dɸ/dt = (πr²)dB/dt

Current induced in the loop,

I=e/R=(πr²)(dB/dt)m/(4π²r²∂ρ)

I= m/(4π∂ρ)db/dt

This was to be proved.