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mina [271]
2 years ago
9

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
Physics
1 answer:
Vedmedyk [2.9K]2 years ago
3 0

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

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