Solve Magnetic Flux from Straight Wire & Rectangular Loop: Wb

AI Thread Summary
A long straight wire carrying a current of 36 A creates a magnetic field affecting a rectangular loop positioned 3 cm away. The magnetic field was initially calculated using the formula B = μ * I / (2πr), yielding a value of 0.00024 T. The area of the rectangular loop was determined to be 0.01125 m², leading to a calculated magnetic flux of 2.70e-6 Wb. However, this approach is incorrect because the magnetic field is not uniform across the loop's area. To accurately find the magnetic flux, it is necessary to integrate the magnetic field over the area of the loop from 3 cm to 10.5 cm.
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Homework Statement


A long straight wire carries a current 36 A. A rectangular loop with two sides parallel to the straight wire has sides 7.5 cm and 15 cm with its near side a distance 3 cm from the straight wire as shown in the figure. The permeability of free space is 4π e -7 T*m/A. Find the magnetic flux through the rectangular loop. Answer in units of Wb.

http://img112.imageshack.us/img112/9541/mblf4.jpg
Shot at 2007-07-31

Homework Equations



Magnetic flux = BA
B = u * I / (2*pi*r)


The Attempt at a Solution



I found the magnetic field

B = u * I / (2*pi*r) = (4*pi*10^-7 * 36 A) / (2*pi * 0.03 m) = 0.00024 T
Then I found the area of the rectangle which A = 0.075 * 0.15 = 0.01125

I multipled BA to get the magnetic flux. My final answer was 2.70e-6 Wb but this answer is wrong. Could someone please tell me what I'm doing wrong? Thank you.
 
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the magnetic field is not constant throughout the area. therefore you have to integrate B*dA, the flux, from r=3 cm to r=3+7.5= 10.5 cm
 

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