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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 = πr 2 Area of cross section = πa 2 Mass of wire, m = (πa 2 ) l ×∂            ……………….(i) Resistance of wire R = ρl/ πa 2 Using (i) ,         R = ρl/(m/l∂) = ρl 2 ∂/m     R= [ρ(2πr) 2 ∂/m = 4π 2 r 2 ∂ρ/m     …………………(ii) Flux through the loop ɸ = BA = B (πr 2 ) E = dɸ/dt = (πr 2 )dB/dt Current induced in the loop, I=e/R=(πr 2 )(dB/dt)m/(4π 2 r 2 ∂ρ) I= m/(4π∂ρ)db/dt This was to be proved.