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For each homework question and lab report we will make a post, this will probably contain a few tips on what the problems are about and how to solve them. If you are stuck on something then instead of emailing us directly you should post a comment in reply to the relevant post. We will try to guide you through tough points and help you understand the problems and the concepts behind them.
Wednesday, September 29, 2010
Chapter 19, Problems 9-12
5 comments:
Muntazim Mukit
said...
I'm having trouble with problem #10. In know that the problem involves the equation for calculating the force per unit length of the magnetic force generated by two current carrying wires: F/l = (permeability of free space constant)(I1)(I2)/ (2*pi*d).
I know that the current is the same, so I1=I2 in the above equation, and the equation can be simplified to: F/l = (permeability of free space constant)(I1)^2/ (2*pi*d). I also have the mass per unit length, m/l (which I calculated to be .044 kg/m in SI units based upon the value given to me 44 g/m) . But I can't seem to calculate the force/unit length.
I tried using another equation, B = (permeability of free space constant) I / (2*pi*R), but I don't know what B is.
I also calculated d based upon the fact that wires form an isosceles triangle, the angle between them is 16 degrees, and using trigonometry. I'll post the value later, since I don't have my scrap work with me right now.
Muntazim Mukit: See my comment to Anonymous for problem # 4, which is Prob. 20 SV8, Ch19, p. 657. WebAssign prob. 10 for Ch19 is SV9, Ch19, Prob. 72, which relates to Section 8 of SV8, Ch19: Magnetic Force Between Two Parallel Conductors. (You saw the video demonstration in lecture last Thursday, so you should already know what direction the currents have to be going to get repulsion.) See my comment below for the useful tip of choosing a convenient length for the two wires, L=1 m, say. Then you calculate the mass of each one from the (linear) density you're given and, from that, calculate the weight W=Mg of each 1 m of wire. So you have two 1 meter pieces of parallel wire that have to be kept apart by a 16 degree angle. Note that they are in equilibrium: they are not moving so their velocity and their acceleration is zero. By F=ma, then, the net force on each wire must be zero. Force is a vector, so it's the vector sum of forces on each wire that is zero. Now, as in PHY 121, you make a free body diagram. "Cut" the supporting string for each wire and put a tension force T into the problem to make up for each cut string. Concentrate on one of the wires and its string, say, the right one looking at the system "end on". You have T going up and to the left, W going down, and the magnetic force going to the right. You need to take relevant components of the forces to get the "x" and "y" component equations for sum of forces = Ma = 0. It helps to take "y" along the string direction and "x" perpendicular to it. This allows you to solve for the "x" component of magnetic force on the right-hand wire needed to balance the "x" component of the weight force of the wire. This gives you a numerical value for the magnetic force. A Ch19 equation gives you a formula for the magnetic force that allows you to solve for the current, actually the square of the current. Take the square root of that and you have the needed current.
Thank you Professor Koch! Your comment was quite helpful. I understood what you were saying and I was able to apply my knowledge of force vectors to determine the magnetic force. Additionally, the way I had calculated d was correct. It is interesting to see problems that not only incorporate Physics II material but Physics I material as well.
I am unsure how to use both currents to solve for the magnetic field.
I presume the equation to use is B=UoI/2R but I am unsure how to relate that to both currents or when to use which when finding the field at the center.
I tried doing the eqn twice and then adding them but to no avail. Can you give me a hint about where I might be going wrong or where I should focus? Thanks alot!
5 comments:
I'm having trouble with problem #10. In know that the problem involves the equation for calculating the force per unit length of the magnetic force generated by two current carrying wires: F/l = (permeability of free space constant)(I1)(I2)/ (2*pi*d).
I know that the current is the same, so I1=I2 in the above equation, and the equation can be simplified to: F/l = (permeability of free space constant)(I1)^2/ (2*pi*d). I also have the mass per unit length, m/l (which I calculated to be .044 kg/m in SI units based upon the value given to me 44 g/m) . But I can't seem to calculate the force/unit length.
I tried using another equation, B = (permeability of free space constant) I / (2*pi*R), but I don't know what B is.
I also calculated d based upon the fact that wires form an isosceles triangle, the angle between them is 16 degrees, and using trigonometry. I'll post the value later, since I don't have my scrap work with me right now.
Any help/guidance/tips?
Muntazim Mukit: See my comment to Anonymous for problem # 4, which is Prob. 20 SV8, Ch19, p. 657. WebAssign prob. 10 for Ch19
is SV9, Ch19, Prob. 72, which relates to Section 8 of SV8, Ch19: Magnetic Force Between Two Parallel Conductors. (You saw
the video demonstration in lecture last Thursday, so you should already know what direction the currents have to be going to
get repulsion.) See my comment below for the useful tip of choosing a convenient length for the two wires, L=1 m, say. Then you calculate the mass of each one from the (linear) density you're given and, from that, calculate the weight W=Mg of each 1 m
of wire. So you have two 1 meter pieces of parallel wire that have to be kept apart by a 16 degree angle. Note that they
are in equilibrium: they are not moving so their velocity and their acceleration is zero. By F=ma, then, the net force on each
wire must be zero. Force is a vector, so it's the vector sum of forces on each wire that is zero. Now, as in PHY 121, you
make a free body diagram. "Cut" the supporting string for each wire and put a tension force T into the problem to make
up for each cut string. Concentrate on one of the wires and its string, say, the right one looking at the system "end on".
You have T going up and to the left, W going down, and the magnetic force going to the right. You need to take relevant
components of the forces to get the "x" and "y" component equations for sum of forces = Ma = 0. It helps to take "y" along
the string direction and "x" perpendicular to it. This allows you to solve for the "x" component of magnetic force on
the right-hand wire needed to balance the "x" component of the weight force of the wire. This gives you a numerical value
for the magnetic force. A Ch19 equation gives you a formula for the magnetic force that allows you to solve for the current,
actually the square of the current. Take the square root of that and you have the needed current.
Thank you Professor Koch! Your comment was quite helpful. I understood what you were saying and I was able to apply my knowledge of force vectors to determine the magnetic force. Additionally, the way I had calculated d was correct. It is interesting to see problems that not only incorporate Physics II material but Physics I material as well.
You're welcome. I assigned this problem because it nicely combines PHY 121 and PHY 122 material, just as you noted.
Hey Professor,
I had a question about number 12.
I am unsure how to use both currents to solve for the magnetic field.
I presume the equation to use is B=UoI/2R but I am unsure how to relate that to both currents or when to use which when finding the field at the center.
I tried doing the eqn twice and then adding them but to no avail. Can you give me a hint about where I might be going wrong or where I should focus? Thanks alot!
-DM
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