Set the ratio of the current I' enclosed by circle 2 to the entire current I equal to the ratio of the area πr2 enclosed by circle 2 to the cross-sectional area πR2 of the wire:

Question

Physics

Finley Pitts

6 November, 16:15

Set the ratio of the current I' enclosed by circle 2 to the entire current I equal to the ratio of the area πr2 enclosed by circle 2 to the cross-sectional area πR2 of the wire:

+2

Answers (1)

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Denise Mercer · Answer 1

This exercise is incomplete, therefore the complete exercise says so: A long, straight wire of radius R carries a steady current I that is uniformly distributed through the cross section of the wire. Calculate the magnetic field a distance r from the centre of the wire in the regions r>=R and r
The answer are

B = (μo*I) / 2pi*r, this is for r> = R

B = ((μo*I*r) / (2pi*R^2)), this for r
Explanation:

The total current that runs through the circle is equal to I and if we use Ampere's law we are left with an expression:

∮B ds = B∮ds = B (2pi*r) = μo*I

Solving for B, we have:

B = (μo*I) / 2pi*r, this is for r> = R

If the interior of the cable, r
I'/I = (pi*r^2) / pi*R^2

Clearing I':

I' = (r^2*I) / R^2

Applying Ampere's law:

∮B ds = B (2pi*r) = μo*I' = μo * ((r^2*I) / R^2)

Solving for B, we have the requested expression:

B = ((μo*I*r) / (2pi*R^2)), this is for r