A long solenoid has 70 text{ turns } cm^{-1} | vedclass

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(B) Given:$n = 70 	ext{ turns } cm^{-1} = 7000 	ext{ turns } m^{-1}$$r = 2.5 	ext{ cm} = 0.025 	ext{ m}$$v = 4.4 	imes 10^6 	ext{ m s}^{-1}$$m =

Vedclass · Accepted Answer

$112.5$

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(B) Given:$n = 70 	ext{ turns } cm^{-1} = 7000 	ext{ turns } m^{-1}$$r = 2.5 	ext{ cm} = 0.025 	ext{ m}$$v = 4.4 	imes 10^6 	ext{ m s}^{-1}$$m = 9 	imes 10^{-31} 	ext{ kg}$$q = 1.6 	imes 10^{-19} 	ext{ C}$The centripetal force required for circular motion is provided by the magnetic Lorentz force:$\frac{mv^2}{r} = qvB$For a long solenoid, the magnetic field $B$ is given by:$B = \mu_0 n I$Substituting $B$ into the force equation:$\frac{mv^2}{r} = qv(\mu_0 n I)$Solving for current $I$:$I = \frac{mv}{q \mu_0 n r}$Substituting the values:$I = \frac{(9 	imes 10^{-31}) 	imes (4.4 	imes 10^6)}{(1.6 	imes 10^{-19}) 	imes (4 \pi 	imes 10^{-7}) 	imes (7000) 	imes (0.025)}$$I = \frac{39.6 	imes 10^{-25}}{1.6 	imes 4 	imes 3.14159 	imes 10^{-7} 	imes 175}$$I = \frac{39.6 	imes 10^{-25}}{3518.57 	imes 10^{-7}} \approx 0.1125 	ext{ A} = 112.5 	ext{ mA}$

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