**Problem 7: A long solenoid with 15 turns / cm has a small loop of area 2.0 cm ^{2} 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.**

**Solution**

**Given data** Number of turns of the solenoid = n = 15/cm = 1500/m

Area of the loop = A = 2.0 cm^{2} = 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 = μ_{0}nI (ii) Δϕ = Δ(BA) (iii) ϵ = (Δϕ)/Δt

Now from the given data, use formula (i),

B_{1} = μ_{0}nI_{1} and B_{2} = μ_{0}nI_{2}, Therefore, ΔB = B_{2} – B_{1} = μ_{0}n(I_{2} – I_{1})

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.

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