An electricity and magnetism problem by Tushar Gopalka

Electricity and Magnetism Level 3

Find the current density as a function of distance r from the axis of a radially symmetrical parallel stream of electrons if the magnetic induction inside the stream varies as $B=b{ r }^{ \alpha }$ , where b, $\alpha$ are positive constants.

None of the above

(b(1+\alpha ){ r }^{ \alpha })/{ \mu }_{ 0 }

(b(1+\alpha ){ r }^{ \alpha -1 })/{ \mu }_{ 0 }

(b\alpha { r }^{ \alpha -1 })/{ \mu }_{ 0 }

1 solution

Ronak Agarwal
Aug 4, 2014

By ampere's law we have :

$B(r)(2\pi r)={ \mu }_{ 0} \int _{ 0 }^{ r }{ J(x)dS } ={ \mu }_{ 0 }\int _{ 0 }^{ r }{ (J(x)2\pi x)dx }$

$\Rightarrow rB(r)={ \mu }_{ 0 }\int _{ 0 }^{ r }{ xJ(x)dx }$

Applying newton's leibnit'z rule we have :

$B(r)+r\frac { dB(r) }{ dr } ={ \mu }_{ 0 }rJ(r).$

Putting the values we have :

$b{ r }^{ \alpha }+r(\alpha b{ r }^{ \alpha -1 })={ \mu }_{ 0 }rJ(r)$

$\Rightarrow \boxed { \frac { b{ r }^{ \alpha -1 }(\alpha +1) }{ { \mu }_{ 0 } } =J(r) }$

I have done magnetism part of irodov

Ronak Agarwal - 6 years, 10 months ago

Awesome...Did it exactly the same way. Each and every step same. Do you know this is from Irodov?

Tushar Gopalka - 6 years, 10 months ago

Have you completed Irodov?

Tushar Gopalka - 6 years, 10 months ago

Nope. I have have done till the magnetism part.

Ronak Agarwal - 6 years, 10 months ago

An electricity and magnetism problem by Tushar Gopalka

1 solution

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