Question 274: Magnetism and Matter

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 _______ $\pi \mathrm{cm}$.

Accepted Answer

We know, magnetic field due to solenoid, $$B = {\mu _0}nI$$
where, I = current, $$n = {N \over L}$$ = no. of turns per unit length
$$ \Rightarrow B = {{{\mu _0}NI} \over L}$$
$$ \Rightarrow L = {{{\mu _0}NI} \over B} = {{4\pi  	imes {{10}^{ - 7}} 	imes 200 	imes 0.29} \over {2.9 	imes {{10}^{ - 4}}}}$$
$$ \Rightarrow L = 8\pi  	imes {10^{ - 2}}\,m$$
$$ \Rightarrow L = 8\pi \,cm$$
Hence, answer = 8.

Magnetism and Matter

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

Integer / Numeric Answer Type