A long solenoid has 100 , text{turns/m} and c | vedclass

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(A) The magnetic field inside a long solenoid is given by $B = \mu_0 n i$, where $n = 100 \, 	ext{turns/m}$.For an electron moving in a circular path

Vedclass · Accepted Answer

$3$

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(A) The magnetic field inside a long solenoid is given by $B = \mu_0 n i$, where $n = 100 \, 	ext{turns/m}$.For an electron moving in a circular path of radius $r$ perpendicular to the magnetic field, the magnetic force provides the centripetal force: $qvB = \frac{mv^2}{r}$.Rearranging for $B$, we get $B = \frac{mv}{qr}$.Equating the two expressions for $B$: $\mu_0 n i = \frac{mv}{qr} \Rightarrow i = \frac{mv}{\mu_0 n q r}$.Given values: $m = 9.1 	imes 10^{-31} \, 	ext{kg}$, $v = 0.046 	imes 3 	imes 10^8 \, 	ext{m/s} = 1.38 	imes 10^7 \, 	ext{m/s}$, $q = 1.6 	imes 10^{-19} \, 	ext{C}$, $n = 100 \, 	ext{m}^{-1}$, $r = 0.023 \, 	ext{m}$, and $\mu_0 = 4\pi 	imes 10^{-7} \, 	ext{T}\cdot	ext{m/A}$.Substituting these values: $i = \frac{9.1 	imes 10^{-31} 	imes 1.38 	imes 10^7}{4\pi 	imes 10^{-7} 	imes 100 	imes 1.6 	imes 10^{-19} 	imes 0.023}$.$i = \frac{12.558 	imes 10^{-24}}{4.62 	imes 10^{-24}} \approx 2.718 \, 	ext{A}$.Rounding to the nearest integer, $i \approx 3 \, 	ext{A}$.

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