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.

Solution

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.
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