Question

7) A long straight wire of radius 1.00x10-3 m (1 mm) carries uniform current density J such that the magnetic field at the edge of the wire is 10-5 T. At what distances from the center of the wire is the magnetic field equal to 5x10-6 T? A) 0.5 and 2 mm. B) 2 mm only. C) 0.5 mm only. D) 0.25 and 2 mm. E) 0.25 mm and 2 mm

Answer 1

Answer:A)0.5 and 2 mm

Step-by-step explanation:

Given

radius R of wire is 1 mm

magnetic Field at edge(surface)
`=10^(-5) T`

Magnetic Field at a distance r' from Center is
`B'=5* 10^(-6) T`

and we know

`B=(\mu _0I)/(2\pi r)`

where
`I= current`

`\mu _o=`Permeability of free space

`r=`distance from center

For
`r=R`

`10^(-5)=(\mu _0I)/(2\pi R)`---1

For
`r=r'`

`5* 10^(-6)=(\mu _0I)/(2\pi r')`---2

Divide 1 and 2

`(10^(-5))/(0.5* 10^(-5))=(r')/(R)`

`r'=2 R=2 mm`

If r is inside the wire then

`B=(\mu _0rI)/(2\pi R^2)`

for
`r=R`

`10^(-5)=(\mu _0R\cdot I)/(2\pi R^2)`---3

for
`r=r`

`5* 10^(-6)=(\mu _0r`----4

Divide 3 and 4

`2=(R)/(r`

`r`