Calculating Magnetic Field in a Straight Wire of Radius R with Current I

AI Thread Summary
To calculate the magnetic field inside a straight wire of radius R carrying a uniformly distributed current I, the magnetic field B at a distance r from the center is derived using Ampère's Law. The equation B * 2πr = μ * i_inside relates the magnetic field to the enclosed current. The enclosed current, i_inside, is determined by the ratio of the areas, leading to the formula i_inside = I * (πr^2 / πR^2) = I * (r^2 / R^2). This ratio reflects the proportion of the total current that flows through the area of the imaginary circle (amperian loop) within the wire. The discussion clarifies that understanding this ratio is key to deriving the magnetic field inside the wire.
leelee
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Question:
-straight wire with radius R, carrying current I
-current is uniformly distributed across the cross sectional area of wire
-calculate the magnetic field inside wire as function of distance r from the center of the wire

In the solution, there is a picture of the cross section of the wire, and the current is going into the page, ie X.
there is an imaginary circle, "amperian loop" with radius r, inside the wire.
then, B*2*pi*r = u*i_inside (equation 1)
then somehow i_inside = I*(pi*r^2)/(pi*R^2) = I*r^2/R^2 (equation 2)
This i don't understand. I know it something to do with the fact that current is uniformly distibuted, but how to get equation 2?
Is it just a ratio?
Thanks!
 
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Question has been solved in other forum.
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Yes, it's just the ratio of Areas (inside / entire)
 
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