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Question

(B) The magnetic field $B$ at the centre of a long solenoid is given by the formula $B = \mu_0 n I$, where $n$ is the number of turns per unit length

Vedclass · Accepted Answer

$6.28 	imes 10^{-2} \, Wb/m^2$

Vedclass · Answer

(B) The magnetic field $B$ at the centre of 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:Turns per cm, $n' = 200 \, 	ext{turns/cm} = 200 	imes 10^2 \, 	ext{turns/m} = 2 	imes 10^4 \, 	ext{turns/m}$.Current, $I = 2.5 \, A$.Permeability, $\mu_0 = 4\pi 	imes 10^{-7} \, T \cdot m/A$.Substituting these values into the formula:$B = (4\pi 	imes 10^{-7}) 	imes (2 	imes 10^4) 	imes 2.5$$B = 4\pi 	imes 10^{-7} 	imes 5 	imes 10^4$$B = 20\pi 	imes 10^{-3} \, T$$B = 2 	imes 3.14 	imes 10^{-2} \, T = 6.28 	imes 10^{-2} \, Wb/m^2$.Thus, the correct option is $B$.

$A$ long solenoid has $200$ turns per cm and carries a current of $2.5 \, A$. The magnetic field at its centre is (given $\mu_0 = 4\pi \times 10^{-7} \, T \cdot m/A$):

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