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### Magnetic Field Inside Toroids

Magnetic Field Inside Toroids

Magnetic Field Inside Toroids

### Lesson Explainer: The Magnetic Field due to a Current in a Solenoid ^{[1]}

In this explainer, we will learn how to calculate the magnetic field produced by a current in a solenoid.. Recall the direction of a magnetic field in a loop of a current-carrying wire

The orange line is the magnetic field direction and black line is the wire loop.. The same loop seen from the front, with the magnetic field direction pointing out of the screen, would look like the diagram below.

The magnetic field strength at the center of a loop can be increased by placing more loops in line with it. The diagram below shows two sets of loops with the same current and the same radius lined up in this way.

### [Solved] The magnetic field intensity inside the toroid is B. If the ^{[2]}

The magnetic field intensity inside the toroid is B. If the current in the toroid is doubled then the magnetic field intensity inside the toroid will become:

It can be viewed as a solenoid that has been bent into a circular shape to close on itself.. – The magnetic field B inside the toroid is constant in magnitude for the ideal toroid of closely wound turns.

– The magnetic field B inside the toroid is given as,. Where N = number of turns, I = current, and R = average radius of the toroid

### [Solved] Consider an ideal toroid with an average radius 16.0 cm with ^{[3]}

Consider an ideal toroid with an average radius 16.0 cm with 240 turns. The magnitude of the magnetic field inside the toroid is [(\(\frac{μ_0}{4π}\)) = 10-7 Tm/A:

AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 1). – If a solenoid is bent in a circular shape and the ends are joined, we get a toroid.

– Where μ0 = permeability of vacuum, N = total number of turns, i = current, r = average radius.. Given, average radius, r = 16.0 cm = 0.16 m, N = 240, i = 10 A, \(\frac{μ_0}{4π}\) = 10-7 Tm/A

### 12.7: Solenoids and Toroids ^{[4]}

– Establish a relationship for how the magnetic field of a solenoid varies with distance and current by using both the Biot-Savart law and Ampère’s law. – Establish a relationship for how the magnetic field of a toroid varies with distance and current by using Ampère’s law

In one form or another, they are part of numerous instruments, both large and small. In this section, we examine the magnetic field typical of these devices.

Solenoids are commonly used in experimental research requiring magnetic fields. A solenoid is generally easy to wind, and near its center, its magnetic field is quite uniform and directly proportional to the current in the wire.

### Magnetic field inside a toroidal solenoid is ? ^{[5]}

Hint: Due to a current carrying element, study the formation of magnetic fields. The concept of ampere’s circuital laws as an alternative to Biot Savart Law and the right hand thumb rule to be applied to find there magnetic field from the direction of the current flow

The independent of the radius of the toroid is the magnetic field inside the toroidal solenoid. In the open space inside the magnetic field (point P) and to the toroid (point Q) is zero

Therefore, outside the solenoid’s radius for locations, the magnetic field is zero. Like a solenoid bent a toroid looks the same into a circular shape such as to close itself into a loop like structure.

### Average Magnitude of Magnetic Field inside a Toroidal Coil ^{[6]}

I want to find the average magnitude of magnetic field inside a toriodal coil (I will be using toroidal coil and toroid interchangeably) of a circular cross-section, like this:. $R=$ Radius of the cross-section of the toroid $=\frac{r_2-r_1}{2}$

The plane containing the ring will be called the horizontal plane and the one perpendicular to it will the vertical plane which passes through the center of the toroid.. N is sufficiently large that the magnetic field at a fixed distance from the centre of toroid is constant.

Now, when we ask what is the average magnetic field inside the toroid is usually given as $$B_\text{average} = \frac{\mu_0 NI}{2\pi r_\text{average}}$$. I couldn’t find the derivation of the radius where the magnetic field matches the average magnetic field of the whole toroid, so I tried deriving it myself

### The magnetic field inside a toroidal solenoid is ^{[7]}

So for loop lying inside the solenoid, if is the magnetic field, is the area element, is the radius of the Amperian loop , is the total number of turns on the toroid and is the steady current through each turn,. For Amperian loop chosen inside or outside the toroid total enclosed current is and hence,

Hence, the magnetic field inside a toroidal solenoid is zero.

### What is the magnitude of the magnetic field inside the toroid ^{[8]}

A toroid having a square cross section, 5.00 cm on a side, and an inner radius of 16.0 cm has 600 turns and carries a current of 0.700 A. (It is made up of a square solenoid bent into a doughnut shape.)

(b) What is the magnitude of the magnetic field inside the toroid at the outer radius?. (a) What is the magnitude of the magnetic field inside the toroid at the inner radius?

### 12.6 Solenoids and Toroids – University Physics Volume 2 ^{[9]}

– Establish a relationship for how the magnetic field of a solenoid varies with distance and current by using both the Biot-Savart law and Ampère’s law. – Establish a relationship for how the magnetic field of a toroid varies with distance and current by using Ampère’s law

In one form or another, they are part of numerous instruments, both large and small. In this section, we examine the magnetic field typical of these devices.

Solenoids are commonly used in experimental research requiring magnetic fields. A solenoid is generally easy to wind, and near its center, its magnetic field is quite uniform and directly proportional to the current in the wire.

### Magnetic Fields Produced by Currents: Ampere’s Law ^{[10]}

– Calculate current that produces a magnetic field.. – Use the right hand rule 2 to determine the direction of current or the direction of magnetic field loops.

Indeed, when Oersted discovered in 1820 that a current in a wire affected a compass needle, he was not dealing with extremely large currents. How does the shape of wires carrying current affect the shape of the magnetic field created? We noted earlier that a current loop created a magnetic field similar to that of a bar magnet, but what about a straight wire or a toroid (doughnut)? How is the direction of a current-created field related to the direction of the current? Answers to these questions are explored in this section, together with a brief discussion of the law governing the fields created by currents.

As noted before, one way to explore the direction of a magnetic field is with compasses, as shown for a long straight current-carrying wire in Figure 1. Hall probes can determine the magnitude of the field

### Q49P A toroid having a square cross s… [FREE SOLUTION] ^{[11]}

A toroid having a square cross section, on a side, and an inner radius of has and carries a current of . (It is made up of a square solenoid—instead of a round one as in Figure bent into a doughnut shape.) (a) What is the magnetic field inside the toroid at the inner radius and (b) What is the magnetic field inside the toroid at the outer radius?

b) The magnetic field inside the toroid at the outer radius is. At a point inside the toroid, the magnitude of the magnetic field is given by equation,

Using that equation, we can calculate the magnetic field inside the toroid at the inner and outer radius.. By using equation (i), we can calculate the magnetic field at the inner radius,

### Sources

- https://www.nagwa.com/en/explainers/186157825721/#:~:text=per%20Unit%20Length-,The%20magnetic%20field%20strength%2C%20%F0%9D%90%B5%20%2C%20inside%20the%20center%20of%20a,%EF%8A%AD%20T%E2%8B%85m%2FA.
- https://testbook.com/question-answer/the-magnetic-field-intensity-inside-the-toroid-is–60904e7ae2dafcd0ff142fc1
- https://testbook.com/question-answer/consider-an-ideal-toroid-with-an-average-radius-16–62e833b5182923901f51b9fa
- https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/12%3A_Sources_of_Magnetic_Fields/12.07%3A_Solenoids_and_Toroids
- https://www.vedantu.com/question-answer/magnetic-field-inside-a-toroidal-solenoid-is-class-12-physics-cbse-60ad14ef3811760ea6d12f97
- https://physics.stackexchange.com/questions/536274/average-magnitude-of-magnetic-field-inside-a-toroidal-coil
- https://byjus.com/question-answer/magnetic-field-inside-a-toroidal-solenoid-is/
- https://www.physicsforums.com/threads/what-is-the-magnitude-of-the-magnetic-field-inside-the-toroid.100085/
- https://pressbooks.online.ucf.edu/osuniversityphysics2/chapter/solenoids-and-toroids/
- https://courses.lumenlearning.com/suny-physics/chapter/22-9-magnetic-fields-produced-by-currents-amperes-law/
- https://www.hellovaia.com/textbooks/physics/fundamentals-of-physics-10th-edition/magnetic-fields-due-to-currents/q49p-a-toroid-having-a-square-cross-section-on-a-side-and-an/