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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:

Current: [itex]I_1 = n.i[/itex]

Area of the section: [itex]A_1 = \pi R^2[/itex]

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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