Two long straight wires are parallel to each other and are separated by 78 mm. The current in wire 1 is 3.55 A and the current in wire 2 is 2.75 A. What is the force per unit length between the two wires?

Respuesta :

Answer:

[tex]2.5\cdot 10^{-5}N[/tex]

Explanation:

The force per unit length between two current-carrying wires is given by:

[tex]\frac{F}{L}=\frac{\mu_0 I_1 I_2}{2\pi r}[/tex]

where

[tex]\mu_0[/tex] is the vacuum permeability

[tex]I_1, I_2[/tex] are the two currents

r is the separation between the wires

In this problem, we have

[tex]I_1 =3.55 A[/tex] is the current in the first wire

[tex]I_2 = 2.75 A[/tex] is the current in the second wire

[tex]r=78 mm=0.078 m[/tex] is the separation between the wires

Substituting into the equation, we find

[tex]\frac{F}{L}=\frac{(4\pi \cdot 10^{-7} H/m)(3.55 A)(2.75 A)}{2\pi (0.078 m)}=2.5\cdot 10^{-5}N[/tex]

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