Question

Three long wires are connected to a meter stick and hang down freely. Wire 1 hangs from the 50-cm mark at the center of the meter stick and carries 1.50 A of current upward. Wire 2 hangs from the 70-cm mark and carries 4.00 A of current downward. Wire 3 is to be attached to the meterstick and to carry a specific current, and we want to attach it at a location that results ineach wire experiencing no net force.

(a) Determine the position of wire 3.

Answer 1

Three long wires are connected to a meter stick and hang down freely. Wire 1 hangs from the 50-cm mark at the center of the meter stick and carries 1.50 A of current upward. Wire 2 hangs from the 70-cm mark and carries 4.00 A of current downward. Wire 3 is to be attached to the meterstick and to carry a specific current, and we want to attach it at a location that results ineach wire experiencing no net force.

(a) Determine the position of wire 3.

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

Step-by-step explanation:

a)
`F_(net) \text {on wire }3=0`

`(\mu_0 I_1 I_3)/(2 \pi x) = (\mu I_2 I_3)/(2 \pi (0.2+x)) \\\\(1.5)/(x) =(4)/(0.2+x) \\\\0.03+1.5x=4x\\\\x=0.012m\\\\=1.2cm`

position of wire = 50 - 1.2

= 48.8cm

b)
`F_(net) \text {on wire }1=0`

`(\mu _0 I_1 I_3)/(2 \pi (1.2)) = (\mu _0 I_1 I_2)/(2 \pi (20)) \\\\(I_3)/(1.2) =(4)/(20) \\\\I_3=0.24A`

Direction ⇒ downward