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  • A long walled pipe of radius R carries a current i along its length. The current density is uniform over the circumference of the pipe

A long walled pipe of radius R carries a current i along its length. The current density is uniform over the circumference of the pipe.The magnetic field at the centre of the pipe due to at the quarter potion of the pipe shown, is 

Option: 1

\frac{\mu_0 i \sqrt{2}}{4 \pi^2 R}


Option: 2

\frac{\mu_{0 i}}{\pi^2 R}


Option: 3

\frac{2 \mu_0 i \sqrt{2}}{\pi^2 R}


Option: 4

None


Answers (1)

\lambda=\frac{i}{2 \pi r} \\       

d i=\lambda \cdot R d \theta \\

d B=\frac{\mu_0 \lambda R d \theta}{2 \pi R} \\

B_{\perp}=\int_0^{\pi / 2} d B \sin \theta =\frac{\mu_0 \lambda}{2 \pi}=\frac{\mu_0 i}{4 \pi^2 R} \\

B_{11}=\int_0^{\pi / 2} d B \sin \theta=\frac{\mu_0 i}{4 \pi^2 R} \\

B_{\text {net }}=\sqrt{2} \frac{\mu_0 i}{4 \pi^2 R} \quad\left(\because B_{\text {net }}=\sqrt{\left(B_{\perp}\right)^2+\left(B_{11}\right)^2}\right)

 

Posted by

Kshitij

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