Question 314: Electromagnetic Induction

Question

The self inductance of solenoid of length $$31.4 \mathrm{~cm}$$, area of cross section $$10^{-3} \mathrm{~m}^2$$ having total number of turns 500 will be nearly [$$\mu_0=4 \pi 	imes 10^{-7}$$ SI unit]

Accepted Answer

$$\begin{aligned}
& \ell=31.4 \mathrm{~cm}=0.314 \mathrm{~m} \
& \mathrm{~A}=10^{-3} \mathrm{~m}^2, \mathrm{~N}=500 \
& 	ext { Self induction } \mathrm{L}=\mu_0 \mathrm{n}^2 \ell \mathrm{A} \
& =\frac{\mu_0 \mathrm{~N}^2 \mathrm{~A}}{\ell} \quad 	ext { where } \mathrm{n}=\frac{\mathrm{N}}{\ell} \
& =\frac{4 \pi 	imes 10^{-7} 	imes(500)^2 	imes 10^{-3}}{0.314} \
& =\frac{4 	imes 3.14 	imes 25 	imes 10^{-6}}{0.314} \
& =10^{-3} \mathrm{H} \
&
\end{aligned}$$

Answer

$$3 	imes 10^{-6} \mathrm{H}$$

Answer

$$2 	imes 10^{-6} \mathrm{H}$$

Answer

$$0.5 	imes 10^{-6} \mathrm{H}$$

Answer

$$4 	imes 10^{-6} \mathrm{H}$$

Electromagnetic Induction

The self inductance of solenoid of length $31.4 \mathrm{~cm}, area of cross section 10^{-3} \mathrm{~m}^2 having total number of turns 500 will be nearly [\mu_0=4 \pi \times 10^{-7}$ SI unit]

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