What current must be passed through a solenoi | vedclass

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(A) The magnetic field inside a long solenoid is given by the formula: $B = \mu_0 n i$, where $n$ is the number of turns per unit length and $i$ is th

Vedclass · Accepted Answer

$8$

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(A) The magnetic field inside a long solenoid is given by the formula: $B = \mu_0 n i$, where $n$ is the number of turns per unit length and $i$ is the current.Given: $n = 20 	ext{ turns/cm} = 2000 	ext{ turns/m}$.Given: $B = 20 	ext{ mT} = 20 	imes 10^{-3} 	ext{ T}$.We know $\mu_0 = 4\pi 	imes 10^{-7} 	ext{ T m/A}$.Substituting the values into the formula:$20 	imes 10^{-3} = (4\pi 	imes 10^{-7}) 	imes 2000 	imes i$$20 	imes 10^{-3} = 8\pi 	imes 10^{-4} 	imes i$$i = \frac{20 	imes 10^{-3}}{8\pi 	imes 10^{-4}} = \frac{200}{8\pi} = \frac{25}{\pi} \approx 7.96 	ext{ A}$.Rounding to the nearest integer, the current is $8 	ext{ A}$.

What current must be passed through a solenoid with $20 \text{ turns/cm}$ to produce a magnetic field of $20 \text{ mT}$ (in $\text{ A}$)? (Given: $\frac{\mu_0}{4\pi} = 10^{-7} \text{ T m/A}$)

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