The magnetic field inside a 200 turns solenoid of radius 10 cm is $2.9 imes 10^{-4} \mathrm{Tesla}$. If the solenoid carries a current of 0.29 A, then the length of the solenoid is ________ $\pi~ \mathrm{cm}$.

Question

The magnetic field inside a 200 turns solenoid of radius 10 cm is $2.9 	imes 10^{-4} \mathrm{Tesla}$. If the solenoid carries a current of 0.29 A, then the length of the solenoid is ________ $\pi~ \mathrm{cm}$.

Aicharya · Accepted Answer

Assuming long solenoid
$\begin{aligned}
& \mathrm{B}=\mu_0\left(\frac{\mathrm{~N}}{\ell}\right) \mathrm{i} \\ & \ell=\frac{\mu_0 \mathrm{Ni}}{\mathrm{~B}}=\frac{\left(4 \pi \times 10^{-7}\right)(200)(0.29)}{2.9 \times 10^{-4}} \mathrm{~m} \\ & =8 \pi \mathrm{~cm}
\end{aligned}$

The magnetic field inside a 200 turns solenoid of radius 10 cm is $2.9 \times 10^{-4} \mathrm{Tesla}$. If…

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