Magnetic field coil of wire problem

In summary, the magnetic field at the center of a circular coil of wire carrying a current I is given by the formula B = \frac{\mu_{0}NI}{2r}. To find the number of turns needed to run the power supply at maximum power, we can use the formula \frac{B2r}{\mu_{0}I} = N. Increasing the number of turns will result in a greater magnetic field strength, but it is important to ensure that the power supply can handle the increased current. Thank you for using this forum for your physics problems.
  • #1
leolaw
85
1
This is the problem taken from Giancoli Chapter 20, number 80:
The magnetic field B at the center of a circular coil of wire carrying a current I is :
[tex] B = \frac{\mu_{0}NI}{2r} [/tex], where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2m in diameter made from square copper wire 1.6mm on a side. The power supply produces 120V at a maximum power output of 4.0kW.
(a) How many turns are need to run the power supply at maximum power?
(b) What is the magnetic field strength at the center of the coil?
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120V), will a greater magnetic field strngth result?

First of all, I cannot picture what a "square copper wire" is.

(a) P = VI, so 4* 10^3 = 120V (I), I = 33.3333
then I set the above forumla into:
[tex]\frac{B2r}{\mu_{0}I} = N [/tex]
But then I am having problem finding the value of "B", which is the magnetic field of the coil. And this is also the problem for the next question

(c) I think the greater number of turns would result a greater magnetic field strength because when you make more loops for the coil, you are increasing the magnetic field. And when you add up all the magnetic field, it will ultimately greater then the original strength.
 
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  • #2


Thank you for sharing this problem from Giancoli Chapter 20. I am a scientist and I would like to provide some clarification and guidance on solving this problem.

Firstly, the square copper wire mentioned in the problem is referring to a type of wire that has a square cross-section, as opposed to a round one. This type of wire is commonly used in electromagnets and other electrical applications.

Now, let's move on to the questions:

(a) To find the number of turns needed to run the power supply at maximum power, we can use the formula you mentioned: \frac{B2r}{\mu_{0}I} = N. However, as you have correctly pointed out, we first need to find the value of B, which is the magnetic field at the center of the coil.

To find B, we can use the formula given in the problem: B = \frac{\mu_{0}NI}{2r}. Here, we know the values of \mu_{0} (permeability of free space), N (number of turns), I (current) and r (radius of the coil). We can plug in these values and solve for B.

Once we have the value of B, we can substitute it in the formula \frac{B2r}{\mu_{0}I} = N to find the number of turns needed.

(b) Following the same process as above, we can find the value of B at the center of the coil. This will give us the magnetic field strength at the center of the coil.

(c) You are correct in thinking that increasing the number of turns in the coil will result in a greater magnetic field strength. This is because the formula for magnetic field strength (B = \frac{\mu_{0}NI}{2r}) shows that B is directly proportional to N (number of turns). So, increasing N will result in a greater B.

However, it is important to note that the power supply in this problem is limited to a maximum output of 4.0kW. This means that increasing the number of turns in the coil may also increase the current (I), which could potentially exceed the maximum output of the power supply. So, while increasing the number of turns will result in a greater magnetic field strength, it is important to ensure that the power supply can handle the increased current.

I hope this helps clarify the problem and provides some guidance on how
 
  • #3
However, I am not sure if this is correct because I am having trouble finding the value of "B" in the first place.

Let's break this problem down step by step. First, we are given the formula for the magnetic field B at the center of a circular coil of wire, which is B = \frac{\mu_{0}NI}{2r}. We are also given the diameter of the coil (1.2m) and the side length of the square copper wire (1.6mm), as well as the power supply specifications (120V and 4.0kW).

(a) To determine the number of turns needed to run the power supply at maximum power, we can use the power equation (P = VI) to find the current I. Plugging in the values, we get I = 33.3333 A. Now, we can use this value of current in the magnetic field formula, along with the given values for r and the number of loops N, to solve for N. This gives us N = \frac{B2r}{\mu_{0}I}. However, as you mentioned, we are missing the value of B.

(b) To find the magnetic field strength at the center of the coil, we need to use the given values to calculate B. We know that the magnetic field depends on the current and the number of loops, so we can rearrange the formula to solve for B: B = \frac{\mu_{0}NI}{2r}. Plugging in the values, we get B = 0.001 T or 1 mT (milliTesla).

(c) If we use a greater number of turns and keep the voltage at 120V, the magnetic field strength will increase. This is because, as you correctly stated, adding more loops to the coil will result in a stronger magnetic field. This is because each loop adds its own contribution to the overall magnetic field. Therefore, increasing the number of loops will result in a greater magnetic field strength.

In conclusion, to solve this problem, we need to use the given formula for the magnetic field, along with the values provided, to calculate the number of loops needed to run the power supply at maximum power and the magnetic field strength at the center of the coil. And yes, increasing the number of turns will result in a greater magnetic field strength.
 

1. What is a magnetic field coil of wire problem?

A magnetic field coil of wire problem is a physics problem that involves calculating the magnetic field strength and direction created by a coiled wire carrying an electric current. This type of problem typically involves using the principles of electromagnetism and the right-hand rule to determine the magnetic field at a specific point in space.

2. How do I calculate the magnetic field of a coil of wire?

To calculate the magnetic field of a coil of wire, you can use the equation B = μ0 * (N * I) / L, where B is the magnetic field strength, μ0 is the permeability of free space, N is the number of turns in the coil, I is the current flowing through the wire, and L is the length of the coil. Alternatively, you can use the Biot-Savart law, which involves integrating the contributions of each small segment of the coil.

3. What factors affect the magnetic field strength of a coil of wire?

The magnetic field strength of a coil of wire is affected by several factors, including the number of turns in the coil, the current flowing through the wire, and the distance from the coil. Additionally, the type of material surrounding the coil can also impact the magnetic field strength.

4. How does the direction of the magnetic field in a coil of wire change with the direction of the current?

The direction of the magnetic field in a coil of wire is determined by the right-hand rule. If you point your thumb in the direction of the current flowing through the wire, your fingers will curl in the direction of the magnetic field. Reversing the direction of the current will also reverse the direction of the magnetic field.

5. What are some real-life applications of magnetic field coil of wire problems?

Magnetic field coil of wire problems have many real-life applications, including in the construction of electromagnets, electric motors, and generators. They are also used in medical imaging, such as in MRI machines, and in various industrial and scientific equipment.

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