Problem 7: A long solenoid with 15 turns / cm has a small loop of area 2.0 cm2 placed inside the solenoid normal to its axis. If the current created by the solenoid changes steady from 2.0 A to 4.0 Amp in 0.1 s. What is the induced emf in the loop when the current is changing.
Given data Number of turns of the solenoid = n = 15/cm = 1500/m
Area of the loop = A = 2.0 cm2 = 2.0 × (10-2)2 = 2.0 × 10-4 m
Change in current = ∆I = 4.0 – 2.0 = 2.0 A
Time required for the change in the current = 0.1 s
Required data Induced emf = ε =?
Formulae (i) B = μ0nI (ii) Δϕ = Δ(BA) (iii) ϵ = (Δϕ)/Δt
Now from the given data, use formula (i),
B1 = μ0nI1 and B2 = μ0nI2, Therefore, ΔB = B2 – B1 = μ0n(I2 – I1)
Now use formula (ii), Δϕ = AΔB … (Since area A is constant and can be taken out). Put the values from the given data,
Now apply formula (iii) to find the induced emf.