How to Calculate the Magnetic Field in a Toroid?

In summary, the problem involves finding the magnitude of the magnetic field in a toroid with a wire carrying a current of 7.80 Amperes and wrapped around it 920 times. The inner and outer radii of the toroid are 14.0 cm and 16.8 cm, respectively. The equation used is B=μ0NI/2πr, where B is the magnetic field, μ0 is the permeability constant, N is the number of times the wire is wrapped, I is the current, and r is the radius. To find the field in the middle of the toroid, the radius should be set to halfway between the inner and outer radii. Setting r=14+2.
  • #1
swashbuckler77
5
0

Homework Statement


"The toroid shown in the figure has a wire carrying a current I= 7.80 Amperes wrapped around it N= 920 times. The inner radius is R1 14.0 cm and outer radius R2 16.8cm. What is the magnitude of the magnetic field along a circle that is halfway between the inner and outer edges of the toroid?"
mUWRfoX.gif


Homework Equations


Magnetic field of a Toroid: B=μ0NI/2πr
B=magnetic field
μ0=permeability constant=4πx10-7 N/A2
N=number of times the wire is wrapped around the toroid
I=current
r=radius

The Attempt at a Solution


Since the problem is asking for the field in the middle of the toroid, I decided to set my radius to halfway between the outside and inside:
16.8 cm-14 cm=2.8 cm
r=14+2.8 cm=.168 m

When I plug in this and all the variables given to me, my answer comes up wrong. Is there a concept I'm missing? My class never covered toroids so I'm pretty much on my own for this one.

Thanks!
 
Last edited:
Physics news on Phys.org
  • #2
So according to the rules I can bump the thread once after 24 hours has passed since the initial post was created? Sorry, I just really need help on this. Is it because the question is so easy to everyone else that it should be obvious what I'm doing wrong? I feel so dumb not knowing how to do this...
 
  • #3
swashbuckler77 said:

Homework Statement


"The toroid shown in the figure has a wire carrying a current I= 7.80 Amperes wrapped around it N= 920 times. The inner radius is R1 14.0 cm and outer radius R2 16.8cm. What is the magnitude of the magnetic field along a circle that is halfway between the inner and outer edges of the toroid?"
mUWRfoX.gif


Homework Equations


Magnetic field of a Toroid: B=μ0NI/2πr
B=magnetic field
μ0=permeability constant=4πx10-7 N/A2
N=number of times the wire is wrapped around the toroid
I=current
r=radius


The Attempt at a Solution


Since the problem is asking for the field in the middle of the toroid, I decided to set my radius to halfway between the outside and inside:
16.8 cm-14 cm=2.8 cm
r=14+2.8 cm=.168 m

Hey man, instead of in the middle you just wound up back at the outer radius for your value of r!

Compute r again.
 

1. What is a toroid?

A toroid is a doughnut-shaped object with a circular cross-section. In physics, it is commonly used to refer to a circular coil of wire that has been wound into a donut shape.

2. How is a toroid different from a solenoid?

While both a toroid and a solenoid are coils of wire, they have different shapes. A solenoid is a long, thin coil that looks like a cylinder, while a toroid is a shorter, wider coil that looks like a donut. Additionally, the magnetic field in a toroid is confined to the inside of the coil, while in a solenoid it extends outside the coil.

3. What is the purpose of a toroid in an electrical circuit?

A toroid is often used in electrical circuits as an inductor, which is a component that can store and release electrical energy. The toroid's circular shape and the fact that the magnetic field is confined to the inside of the coil make it ideal for creating a strong, uniform magnetic field.

4. How is the magnetic field of a toroid calculated?

The magnetic field of a toroid can be calculated using the formula B = (μ0 * N * I) / (2πr), where μ0 is the permeability of free space, N is the number of turns in the coil, I is the current flowing through the coil, and r is the radius of the toroid. This formula assumes that the toroid has a uniform current and is made of a material with high permeability.

5. How does the magnetic field of a toroid affect nearby objects?

The magnetic field of a toroid can induce a current in nearby conductive objects, which can cause interference in electronic devices. It can also cause ferromagnetic objects to be attracted to or repelled from the toroid. The strength of the magnetic field is dependent on the current and number of turns in the coil, so it can be controlled by adjusting these parameters.

Similar threads

What Surface Does ds Represent in Calculating Magnetic Flux Through a Toroid?
    • Introductory Physics Homework Help
Replies
2
Views
3K
Magnetic Field Inside a Toroid
    • Introductory Physics Homework Help
Replies
3
Views
6K
Magnetic energy density, and pressure due to magnetic force
    • Introductory Physics Homework Help
Replies
23
Views
2K
How Do You Calculate Mutual Inductance in Toroidal Solenoids?
    • Introductory Physics Homework Help
Replies
17
Views
4K
Calculating the B field in a small gap in a toroid
    • Introductory Physics Homework Help
Replies
8
Views
13K
How to Calculate the Magnetic Field in a Toroid?
    • Introductory Physics Homework Help
Replies
1
Views
3K
Magnetic field at centre and inside the toroid
    • Introductory Physics Homework Help
Replies
6
Views
5K
Electricity and magnetism (magnitude of magnetic field)
    • Introductory Physics Homework Help
Replies
7
Views
4K
Magnetic field in the gap of a tapered torus
    • Introductory Physics Homework Help
Replies
9
Views
3K
Find field intensity at center of toroid?
    • Introductory Physics Homework Help
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top