6. [1pt] A long horizontal wire carries a current of I 44.3 A. A second wire (l

Question

6. [1pt] A long horizontal wire carries a current of I 44.3 A. A second wire (l 6.36x103 A, parallel to IT), made of 2.20 mm diameter copper wire and parallel to the first but a distance L below it, is held in suspension magnetically, as seen in the figure below. (This means the upwards magnetic force on that lower wire is just large enough to hold it up against its own weight) What is the distance L between the wires? (The density of copper is 8.9E3 kg/m3) Answer Submit All Answers Last Answer: 5.02x10 8 A

Explanation / Answer

magnetic field due to IT at the location of I

B = uo*IT/(2*pi*L)

magnetic force acting per unit length Fb = I*B = u0*IT*I/(2*Pi*L)

mass of wire m = D*V = D*pi*r^2*l

mass per unit length m/l = D*pi*r^2

gravitaitonal force per unit length Fg = (m/l)*g = D*pi*r^2*g

r = radius = 2.2/2 = 1.1 mm = 1.1*10^-3 m

D = density = 8.9*10^3 kg/m^3

the lower wire is suspended

the net force = 0

Fb - Fg = 0

Fb = Fg

uo*IT*I/(2*pi*L) = D*pi*r^2*g

4*pi*10^-7*44.3*6.36*10^3/(2*pi*L) = 8.9*10^3*pi*(1.1*10^-3)^2*9.8

length L = 0.170 m

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