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A long wire is known to have a radius greater than 10.0 mm and less 20 mm, carry a current uniformly distributed over its cross section. If the magnitude of the magnetic field is 3 mT at a point 6.0 mm from the axis of the wire and 1.50 mT at a point 20 mm from the axis, what is the radius of the wire?

Respuesta :

Answer:

Radius = 7.75 mm

Explanation:

magnetic field inside a point in the wire is given as

[tex]B = \frac{\mu_0 i r}{2\pi R^2}[/tex]

now we have

[tex]3mT = \frac{\mu_0 i (6mm)}{2\pi R^2}[/tex]

now outside wire magnetic field is given as

[tex]B = \frac{\mu_0 i}{2\pi r}[/tex]

now we have

[tex]1.50 mT = \frac{\mu_0 i}{2\pi(20 mm)}[/tex]

now divide above two equations

[tex]2 = \frac{6 mm\times 20 mm}{R^2}[/tex]

[tex]R = 7.75 mm[/tex]

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