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  • An air cored solenoid with length 20 cm, area of cross section  a

An air cored solenoid with length 20 cm, area of cross section \mathrm{20\; cm^{2}} and number of turns 400 carries a current 2 A. The current is suddenly switched off within \mathrm{10^{-3}\; s}. The average back emf induced across the ends of the open switch in the circuit is (ignore the variation in magnetic field near the ends of the solenoid)

Option: 1

2 V


Option: 2

4 V


Option: 3

3 V


Option: 4

5 V


Answers (1)

best_answer

\mathrm{\text { Here, } l=20 \mathrm{~cm}=20 \times 10^{-2} \mathrm{~m}, \mathrm{~A}=20 \mathrm{~cm}^2=20 \times 10^{-4} \mathrm{~m}^2, \mathrm{~N}=400, \mathrm{I}_1=2 \mathrm{~A}, \mathrm{I}_2=0, \mathrm{dt}=10^{-3} \mathrm{~s}}

\mathrm{\begin{aligned} \text { As } \varepsilon & =\frac{\mathrm{d} \phi}{\mathrm{dt}}=\frac{\mathrm{d}(\mathrm{BAN})}{\mathrm{dt}} \\ & =\frac{\mu_0 \mathrm{NdIAN}}{l \mathrm{dt}} \quad\left(\because \quad \mathrm{B}=\frac{\mu_0 \mathrm{NI}}{l}\right) \\ & =\frac{\mu_0 \mathrm{~N}\left(\mathrm{I}_1-\mathrm{I}_2\right) \mathrm{AN}}{l \mathrm{dt}} \\ & =\frac{4 \pi \times 10^{-7} \times(400)^2 \times 2 \times 20 \times 10^{-4}}{20 \times 10^{-2} \times 10^{-3}}=4 \mathrm{~V} \end{aligned}}

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avinash.dongre

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