Coaxial Cable!

Consider a co-axial cable which consists of an inner wire of radius $a$ surrounded by an outer shell of inner and outer radii $b$ and $c$ respectively. The inner wire carries a current $I$ and outer shell carries an equal and opposite current. The magnetic field at a distance $x$ from the axis where $b<x<c$ is

$(a)$ $\frac{\mu_{0} I(c^2 - b^2)}{2 \pi x(c^2 - a^2)}$

$(b)$ $\frac{\mu_{0} I(c^2 - x^2)}{2 \pi x(c^2 - a^2)}$

$(c)$ $\frac{\mu_{0} I(c^2 - x^2)}{2 \pi x(c^2 - b^2)}$

$(d)$ $0$

Easy Math Editor

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Comments

This question is based on the application of Ampere's circuital law. Give it a try at least. :)

Pranav Arora - 8 years ago

thnx buddy bt i had already done it... it was the question that i felt was good to be posted because i got stuck in this particular question!!!!

Advitiya Brijesh - 8 years ago

with your help... :)

Advitiya Brijesh - 8 years ago

hey... Is your AGE = 14 ...................?? Please Reply

Vamsi Krishna Appili - 8 years ago

the answer will be C

Farhan Masood Laskar - 8 years ago

I think it will be option c)!!!

Subhrodipto Basu Choudhury - 8 years ago

Sorry, option b)!!!

Subhrodipto Basu Choudhury - 8 years ago

Ramon Vicente Marquez - 8 years ago

magnetic field due to inner wire: mu I / (2 pi x)

current between b and x: - I (x^2 - b^2) / (c^2 - b^2)

magnetic field due to current between b and x: - [mu I / (2 pi x)] [(x^2 - b^2) / (c^2 - b^2)]

magnetic field at x: [mu I / (2 pi x)] [(c^2 - x^2) / (c^2 - b^2)] which is C

Ramon Vicente Marquez - 8 years ago

Ah Ramon, I was waiting for Advitiya to post his attempt. You should not have given the solution. It would be a great experience for Advitiya if he solved this by himself. :)

Pranav Arora - 8 years ago

i rarely give away full solutions. usually i just give hints. i just feel like giving the solution this time.

Ramon Vicente Marquez - 8 years ago

@Ramon Vicente Marquez – hints...this doesn't even require any hint!!

sudheesh srivastava - 8 years ago

8.02x, huh?

Ahaan Rungta - 8 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$