Question

In: Physics

Three long wires are all parallel to each other and are all in the xy plane....

Three long wires are all parallel to each other and are all in the xy plane. Wire 1 runs along the y axis and carries a current of 1.64 A in the +y direction. Wire 2 runs along the

x = 25.0 cm

line and carries a current of 4.04 A in the −y direction.

(a) Determine the location of wire 3 on the x axis so that when it carries a certain current (to be determined later) each wire experiences no net force.

(b) Determine the magnitude and direction of the current in wire 3.

magnitude ?

direction?

Solutions

Expert Solution

Suppose the wire is to the left of origin at a distance d on x-axis and parallel to the y-axis , then it must balance the attractive force between wire 1 and 2. Balancing the forces on wire 1

$F_{12} = F_{13}$

$\frac{\mu _{o}I_{1}I_{2}}{2\pi r} = \frac{\mu _{o}I_{1}I_{3}}{2\pi d}$

$\frac{I_{2}}{r} = \frac{I_{3}}{d}$

$\frac{4.04}{25} = \frac{I_{3}}{d}$

$\frac{I_{3}}{d} = 0.1616$ ..................(1)

Balancing forces on wire 2

$F_{21} = F_{23}$

$\frac{\mu _{o}I_{1}I_{2}}{2\pi r} = \frac{\mu _{o}I_{2}I_{3}}{2\pi (d+25)}$

$\frac{I_{1}}{r} = \frac{I_{3}}{d+25}$

$\frac{1.64}{25} = \frac{I_{3}}{d +25}$

$\frac{I_{3}}{d +25} = 0.0656$ .................(2)

Dividing equation 1 and 2 we get

$\frac{d}{d +25} = \frac{0.0656}{0.1616}$

2.46d = d + 25

1.46d = 25

d = 17.12 cm

The wire must be at x = -17.12 cm

b) Putting value of d in (1)

$\frac{I_{3}}{d} = 0.1616$

I₃ = 0.1616 d =0.1616(17.13)

I₃ = 2.77 A

the current must be along negative y-axis. This is because if two wires have the same current direction they attract each other and if they have opposite current direction they repel each other.

genius_generous answered 1 year ago

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