An air-cored solenoid with length 30 cm, area of cross-section 25 `"cm"^{2}` and number of turns 800, carries a current of 2.5 A. The current is suddenly switched off in a brief time of `10^{-3}`s. Ignoring the variation in magnetic field near the ends of the solenoid, the average back emf induced across the ends of the open switch in the circuit would be .
(i) zero
(ii)3.125 volts
(iii) 6.54 volts
(iv) 16.74 volts
(ii)3.125 volts
(iii) 6.54 volts
(iv) 16.74 volts
(iv) 16.74 volts
Explanation:
An air-cored solenoid with length 30 cm, area of cross-section 25 `"cm"^{2}` and number of turns 800, carries a current of 2.5 A. The current is suddenly switched off in a brief time of `10^{-3}`s. Ignoring the variation in magnetic field near the ends of the solenoid, the average back emf induced across the ends of the open switch in the circuit would be 16.74 volts .
B = μ。`\frac{"N"}{"l"}"l"'`
Flux linked with ‘N’ turns
Initial flux `\phi_{1}` = NBA = Nμ。`\frac{"N"}{"l"}"lA"`
= Nμ。`\frac{"N"}{"l"}"lA"`
=`\frac{4\pi \times10^{-7}\times800\times800\times2.5\times2.5\times10^{-4}}{0.30}`
= ` 16.74\times 10^{-3}`Wb
Final flux `\phi_{2}` = 0
Average back emf |e| = `\frac{d\phi}{dt}`
= `\frac{16.74\times 10^{-3}-0}{10^{-3}}`
= 16.74 V
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