number 9 In an old twist of events, I lack a ruler but do have a pair of wires,
ID: 1450650 • Letter: N
Question
number 9
In an old twist of events, I lack a ruler but do have a pair of wires, a power supply, and an ammeter. I know that if I run a current through the wires I can balance the downward force of gravity on the top wire with the repulsive magnetic force between them. I know the weight per unit length of the wires is 0.12 N/m. I can use the power supply and the ammeter to choose the current (assumed to be the same current in each wire). What value of current should I choose to make the distance between the two wires equal to exactly 1.00 cm? Note that these are parallel wires and not a single wire in an external magnetic field! Some day, you will be done with taking physics. Until then, you keep making electrical gadgets and cursing yourself because Dr. Miller keeps asking you to solve problems involving these gadgets. You wrap 20-gauge copper wire around a toilet paper tube (the tube has a diameter of 4.00 cm and a height of 11.2 cm) to make a solenoid. The wire has a cross sectional area of 1.02 times 10^-6 m^2 and the resistivity of copper is rho = 1.7 times 10^-8 ohm m. If your solenoid has 100 loops, (a) determine tile current required to produce a magnetic field of 6.50 mT at the center of your solenoid, and (b) the power required to deliver this magnetic field.Explanation / Answer
let,
m*g/l=0.12 N/m
separation between wire is r=1cm
use,
magentic force F=i*l*B
m*g=i*l*B
m*g=i*l*(uo*i/2pi*r)
(m*g/l)=uo*i^2/(2pi*r)
0.12=4pi*10^-7*i^2/(2pi*0.01)
===> i=77.46 A
current in the wire, i=77.46 A
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