Magnetic Field due to a current carrying wire

AI Thread Summary
The discussion focuses on calculating the magnetic field at a point on the x-axis due to a short current-carrying wire. A 2.0 cm wire carrying a 20 A current in the positive y direction is analyzed, with the magnetic field calculated at x = 5.0 m. The initial calculation using the formula B = μI/(2πR) yields 8e-7 T, which is incorrect for this scenario. The correct answer is 1.6 nT in the negative z direction, highlighting that the formula applies only to long wires relative to the distance from the field point. This emphasizes the importance of considering wire length in magnetic field calculations.
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Homework Statement


A 2.0 cm length of wire centered on the origin caries a 20 A current directed in the positive y direction. Determine the magnetic field at the point x = 5.0 m on the x-axis.


Homework Equations


B = uI/2piR


The Attempt at a Solution


Using the equation above I just plugged in 5m for R and 20A for I and I got 8e-7 T. I was looked up current in a straight wire and found a calculator in hyperphysics that gave me 8e-7 as well, but the answer that was given to me is 1.6nT in the negative z direction.
 
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The formula B = ##\mu_0##I/(2##\pi##R) is only for a straight wire that is much longer than the distance from the wire to the field point. You have the opposite case where the wire is much shorter than the distance from the wire to the field point.
 

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