Finding current of circular (toroidal) solenoid

In summary, the current in a circular (toroidal) solenoid can be determined using Ampère's Law, which relates the magnetic field inside the solenoid to the current flowing through it. The magnetic field within the toroid is uniform and is given by the formula \( B = \frac{\mu_0 n I}{2\pi r} \), where \( \mu_0 \) is the permeability of free space, \( n \) is the number of turns per unit length, \( I \) is the current, and \( r \) is the distance from the center of the toroid. By rearranging this equation, one can solve for the current \( I \) if the magnetic field \( B \)
  • #1
Grandpa04
2
3
Homework Statement
A circular solenoid has a magnetic field of 1.4 T. The solenoid has 900 turns, a radius of 2 cm, and a length of 70 cm. What is the current running through the solenoid.
Relevant Equations
B = µ*N*I/2πr
I assumed that the radius is referring to a major R like in the image below.
selenoid1.png

I plugged all the values (except for length) into the equation B = µ*N*I/2πr to get 155.6 A for the current value. I am unsure if this is the correct value or if radius refers to minor r of solenoid, in which case a different equation is used.

mimxrtor.png
 
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  • #2
Where does it say that it has a toroidal shape?
 
  • #3
nasu said:
Where does it say that it has a toroidal shape?
Yes, "circular" is ambiguous. Could mean toroidal or cylindrical.
A "length" of 70cm and 900 turns gives less than 1mm per turn, so the length must be along the axis, not the length of wire. If toroidal, that implies a major radius of 70cm/(2π).
 
  • #4
The expression "circular solenoid" is not uncommon for a cylindrical one. It refers to the cross-section. The radius is not useful unless there is a question about the flux.
 
  • #5
nasu said:
The expression "circular solenoid" is not uncommon for a cylindrical one. It refers to the cross-section. The radius is not useful unless there is a question about the flux.
Useful to know, thanks.
 

FAQ: Finding current of circular (toroidal) solenoid

What is a toroidal solenoid?

A toroidal solenoid is a coil of wire, typically wound in a circular or donut-shaped (toroidal) form, which creates a magnetic field when an electric current passes through it. This configuration confines the magnetic field within the core of the toroid, minimizing external magnetic fields.

How do you calculate the magnetic field inside a toroidal solenoid?

The magnetic field inside a toroidal solenoid can be calculated using the formula \( B = \frac{\mu_0 N I}{2 \pi r} \), where \( B \) is the magnetic field, \( \mu_0 \) is the permeability of free space, \( N \) is the number of turns of the coil, \( I \) is the current, and \( r \) is the mean radius of the toroid.

What is the formula to find the current in a toroidal solenoid?

The current \( I \) in a toroidal solenoid can be found using the rearranged magnetic field formula: \( I = \frac{B \cdot 2 \pi r}{\mu_0 N} \), where \( B \) is the magnetic field, \( r \) is the mean radius, \( \mu_0 \) is the permeability of free space, and \( N \) is the number of turns.

What factors affect the current in a toroidal solenoid?

The current in a toroidal solenoid is affected by the magnetic field strength \( B \), the number of turns \( N \), the mean radius \( r \) of the toroid, and the permeability of the core material \( \mu_0 \). Changes in any of these factors will alter the current required to produce a given magnetic field.

How does the core material of a toroidal solenoid influence the current calculation?

The core material of a toroidal solenoid influences the current calculation through its permeability. If the core is made of a material with higher permeability than free space (such as iron), the magnetic field strength for a given current will be higher, reducing the required current for a specific magnetic field. The formula \( I = \frac{B \cdot 2 \pi r}{\mu N} \) can be used, where \( \mu \) is the permeability of the core material instead of \( \mu_0 \).

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