A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?
Number of turns on the solenoid = 15 turns/cm = 1500 turns/m Number of turns per unit length, n = 1500 turns The solenoid has a small loop of area, A =2.0cm2 Current carried by the solenoid changes from 2 A to 4 A. Change in current in the solenoid, di=4−2=2A Change in time, dt=0.1s Induced emf in the solenoid is given by Faraday’s law as: e=dtdϕ ...(i) Where, ϕ= Induced flux through the small loop =BA ... (ii) B= Magnetic field =μ0ni ...(iii) μ0= Permeability of free space =4π×10−7H/m Hence, equation (i) reduces to: e=dtd(BA) =Aμ0n×(dtdi) =2×10−4×4π×10−7×1500×0.12 =7.54×10−6V Hence, the induced voltage in the loop is 7.54×10−6V.
