- #1
flyingpig
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Homework Statement
OKay, PF again erased my hard 30mins work of LaTeX and wouldn't let me backspace. So I apologize if I miss any crucial detail
Two parallel rails with negligible resistance are 10.0 cm apart and are connected by a 5.00 resistor. The circuit also contains two metal rods having resistances of R = 10.0Ω and 15.0 Ω sliding along the rails. The rods are pulled away from the resistor at constant speeds 4.00 m/s and 2.00m/s, respectively. A uniform magnetic field of magnitude 0.0100 T is applied perpendicular to the plane of the rails. Determine the magnitude and direction of the current in the 5.00 Ωresistor
The Attempt at a Solution
http://img219.imageshack.us/img219/7499/p3131alt.th.gif
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So I did my loop
Left Loop [tex]-I_1 R_1 - Blv_1 - I_1 R_3 + I_2 R_3 = 0[/tex]
Right Loop [tex]-Blv_2 - I_2 R_2 - I_2 R_3 + I_1 R_3 = 0[/tex]
Add some numbers
Left Loop [tex]-15I_1 + 5_2 = 4Bl[/tex]
Right Loop [tex]5I_1 - 20I_2 = 2Bl[/tex]
[tex]\begin{bmatrix}
-15 & 5& 4\\
5&-20 & 2
\end{bmatrix}[/tex]
[tex]\begin{bmatrix}
1 & 0& \frac{-18}{55}\\
0& 1 & \frac{-10}{55}
\end{bmatrix}[/tex]
So I1 = 18/55A and I2 = 10/55A
So the current down the middle resistor must be 8/55A which is 0.145A
Here is the book solution
http://img853.imageshack.us/img853/9262/81989521.th.gif
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I didn't even use the 10cm...
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