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

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 $B'=5\times 10^{-6} T$

and we know

$B=\frac{\mu _0I}{2\pi r}$

where $I= current$

$\mu _o=$Permeability of free space

$r=$distance from center

For $r=R$

$10^{-5}=\frac{\mu _0I}{2\pi R}$---1

For $r=r'$

$5\times 10^{-6}=\frac{\mu _0I}{2\pi r'}$---2

Divide 1 and 2

$\frac{10^{-5}}{0.5\times 10^{-5}}=\frac{r'}{R}$

$r'=2 R=2 mm$

If r is inside the wire then

$B=\frac{\mu _0rI}{2\pi R^2}$

for $r=R$

$10^{-5}=\frac{\mu _0R\cdot I}{2\pi R^2}$---3

for $r=r"$

$5\times 10^{-6}=\frac{\mu _0r"I}{2\pi R^2}$----4

Divide 3 and 4

$2=\frac{R}{r"}$

$r"=0.5 mm$