Magnetic field of cylinder with coils problem?

[asdf12312]

Homework Statement

In the picture in the figure, three coils are tightly wrapped around a non-magnetic cylinder of diameter Dcyl. Each coil is defined through the diameter of each wire comprising the coil, dcoil1-dcoil3, the current going through each coil, I1-I3, and the number of turns in each coil, N1 – N3. In addition, each coil extends a length equal to a 1/3 the length of the cylinder. Write a program that defines the magnetic field in the centerline of the cylinder (on the z axis) and plots it against z (from –l to l, where l is the length of the cylinder). Note that the cylinder extends from –l/2 to l/2.

The user inputs values for Dcyl, dcoil1, dcoil2, dcoil3, N1, N2, N3, I1, I2, I3, and l.

The program outputs a graph of Bz vs z from –l to l for:
1. All coils identical – same current I, same diameter, same number of coils. This should give you an answer identical to the case of one coil with current I and number of coils equal to 3N. Confirm.

2. Each coil activated separately – so, I1=I while I2=I3=0, etc. If, in each case you use the same I and N to define each coil, how do you expect the results to compare with each other. Are your results reasonable?

3. Two combinations of I1, I2, and I3, including at least one where the currents are going in different directions.

Homework Equations

The Attempt at a Solution

can someone please help me i don't understand this! I think the magnetic field of cylinder is something like B= u0*I / (2*pi*r) but I'm not sure!

 

[Bystander]

In the picture in the figure, three coils are tightly wrapped around a non-magnetic cylinder of diameter Dcyl. Each coil is defined through the diameter of each wire comprising the coil, dcoil1-dcoil3, the current going through each coil, I1-I3, and the number of turns in each coil, N1 – N3. In addition, each coil extends a length equal to a 1/3 the length of the cylinder. Write a program that defines the magnetic field in the centerline of the cylinder (on the z axis) and plots it against z (from –l to l, where l is the length of the cylinder). Note that the cylinder extends from –l/2 to l/2.

The user inputs values for Dcyl, dcoil1, dcoil2, dcoil3, N1, N2, N3, I1, I2, I3, and l.

The program outputs a graph of Bz vs z from –l to l for:
1. All coils identical – same current I, same diameter, same number of coils. This should give you an answer identical to the case of one coil with current I and number of coils equal to 3N. Confirm.

2. Each coil activated separately – so, I1=I while I2=I3=0, etc. If, in each case you use the same I and N to define each coil, how do you expect the results to compare with each other. Are your results reasonable?

3. Two combinations of I1, I2, and I3, including at least one where the currents are going in different directions.

Homework Equations

I've highlighted the starting points for you.

I think the magnetic field of cylinder is something like B= u0*I / (2*pi*r) but I'm not sure!

Check your class notes or the textbook, or look for "magnetic field of a solenoid" and become sure.

Do not ever let a page long problem statement intimidate you. Just work your way through it one line at a time.

 

[asdf12312]

I guess I'm confused because I don't understand how diameters matter in finding the B field. Also does the Bz = (u0*N*I)/L equation apply to whole cylinder or to each wire/coil too? For part 1) I get if all coils are identical, the B field through each is same so total B field is Bz=B1+B2+B3 or Bz= 3((u0*N*I)/(1/3)) = 9*u0*N*I. this is same answer I also get for case of only one coil with number of coils equal to 3N.

by the way, why do we need the diameters if they don't affect Bz at all?

 

[Bystander]

by the way, why do we need the diameters if they don't affect Bz at all?

Problem statements may be written for you to sort what is necessary from what is not; or to find missing information.

Also does the Bz = (u0*N*I)/L equation apply to whole cylinder or to each wire/coil too?

Yes.

For part 1) I get if all coils are identical, the B field through each is same so total B field is Bz=B1+B2+B3 or Bz= 3((u0*N*I)/(1/3)) = 9*u0*N*I. this is same answer I also get for case of only one coil with number of coils equal to 3N.

Okay, you've "confirmed" part 1.

 

[rezeew]

Hello,

Thank you for your question. The homework problem you have provided involves calculating the magnetic field of a cylinder with coils wrapped around it. This is a common problem in electromagnetism and can be solved using the Biot-Savart law, which states that the magnetic field at a point is proportional to the current and the distance from the point to the current.

To solve this problem, you will need to use the formula B = μ0*I*dL/4*pi*r^2, where μ0 is the permeability of free space, I is the current, dL is the length of the wire, and r is the distance from the point to the wire. You will also need to use the formula for the magnetic field of a solenoid, which is B = μ0*N*I/l, where N is the number of turns and l is the length of the solenoid.

To start, you will need to define the variables and inputs given in the problem, such as the diameter of the cylinder, the diameter of the coils, the number of turns, and the current. Then, you can use these values to calculate the magnetic field at different points along the z-axis, which is the centerline of the cylinder. You will need to use a loop to calculate the magnetic field at different points, starting from -l/2 and going to l/2.

For the first part of the problem, where all the coils are identical, you will need to use the formula for a solenoid to calculate the magnetic field at each point. This should give you the same answer as the case of one coil with a current equal to 3N. This is because the total number of turns in all three coils is equal to 3N, and the magnetic field is directly proportional to the number of turns.

For the second part of the problem, where each coil is activated separately, you will need to use the Biot-Savart law to calculate the magnetic field at each point. In this case, you will need to set the currents of the inactive coils to zero, while keeping the current of the active coil the same. This will allow you to compare the results of each individual coil to the total magnetic field of all three coils.

For the third part of the problem, where different combinations of currents are used, you will need to use the Biot-Savart law to calculate the magnetic field at each point. In this case,