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tiagobt
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Could anyone please help me with the following problem?
A compact package contains n = 100 long straight wires, shaped like a cylinder with a radius of R = 0.500 cm. If each wire conducts i = 2.00 A, calculate the intensity and direction of the magnetic force per unit of length acting on a wire located r = 0.200 cm from the center of the package.
I tried to solve it as follows:
Complete cylinder with radius R
Current: [itex]I_1 = n.i[/itex]
Area of the section: [itex]A_1 = \pi R^2[/itex]
Cylinder with radius r
Current: [itex]I_2[/itex]
Area of the section: [itex]A_2 = \pi r^2[/itex]
[tex]\frac {I_1} {I_2} = \frac {A_1} {A_2}[/tex]
[tex]I_2 = \frac {n i r^2} {R^2}[/tex]
Using Ampère Law for a circle of radius r:
[tex]\oint \vec B \cdot d \vec s = \mu_0 I_2[/tex]
[tex]B 2 \pi r = \frac {\mu_0 n i r^2} {R^2}[/tex]
[tex] B = \frac {\mu_0} {2 \pi} \frac {n i r} {R^2} = 0.0032 T[/tex]
Calculating the force that acts on the wire with distance r from the center:
[tex]F = i l B[/tex]
[tex]\frac F l = iB = 0.0064 N/m = 6.4 mN/m[/tex]
But I was supposed to find [itex]\frac F l = 6.34 mN/m[/itex]. What did I do wrong?
Thanks,
Tiago
A compact package contains n = 100 long straight wires, shaped like a cylinder with a radius of R = 0.500 cm. If each wire conducts i = 2.00 A, calculate the intensity and direction of the magnetic force per unit of length acting on a wire located r = 0.200 cm from the center of the package.
I tried to solve it as follows:
Complete cylinder with radius R
Current: [itex]I_1 = n.i[/itex]
Area of the section: [itex]A_1 = \pi R^2[/itex]
Cylinder with radius r
Current: [itex]I_2[/itex]
Area of the section: [itex]A_2 = \pi r^2[/itex]
[tex]\frac {I_1} {I_2} = \frac {A_1} {A_2}[/tex]
[tex]I_2 = \frac {n i r^2} {R^2}[/tex]
Using Ampère Law for a circle of radius r:
[tex]\oint \vec B \cdot d \vec s = \mu_0 I_2[/tex]
[tex]B 2 \pi r = \frac {\mu_0 n i r^2} {R^2}[/tex]
[tex] B = \frac {\mu_0} {2 \pi} \frac {n i r} {R^2} = 0.0032 T[/tex]
Calculating the force that acts on the wire with distance r from the center:
[tex]F = i l B[/tex]
[tex]\frac F l = iB = 0.0064 N/m = 6.4 mN/m[/tex]
But I was supposed to find [itex]\frac F l = 6.34 mN/m[/itex]. What did I do wrong?
Thanks,
Tiago
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