Magnetostatics - magnetic flux and energy in toroidal inductor

In summary, magnetostatics is the study of static magnetic fields and their effects on charged particles. Magnetic flux is a measure of the strength of a magnetic field passing through a given area. An inductor is a passive electronic component that stores energy in the form of a magnetic field. A toroidal inductor is a type of inductor that is shaped like a doughnut and has advantages such as low electromagnetic interference and high inductance. Energy is stored in a toroidal inductor in the form of a magnetic field, which can be released when the current is disrupted.
  • #1
tigger88
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0

Homework Statement


A toroidal inductor consists of 500 turns of wire on a ring-shaped core of magnetic material with a relative permeability of 8000. The core has a square cross-section with an internal radius of 20mm, external radius of 40mm and height of 20mm.
Find:
a) Magnetic flux in the core
b) Magnetic energy stored in the inductor
when the current in the winding is 50mA

Homework Equations


Magnetic flux = [tex]\int\int[/tex]B.dS
(1) B = [tex]\mu[/tex]0[tex]\mu[/tex]r H
(2) H = (NI)/(2[tex]\pi[/tex]R)
Ampere's Law: [tex]\int[/tex]B.dL = [tex]\mu[/tex]0 I

Energy Um = (1/2)I[tex]\Phi[/tex]

The Attempt at a Solution


a) From (1) and (2), B = [tex]\mu[/tex]0[tex]\mu[/tex]r (NI)/(2[tex]\pi[/tex]R)
where R is the radius from the centre of the torus to the centre of the core.
Magnetic flux = [tex]\Phi[/tex] = B [tex]\int\int[/tex]dS = [tex]\mu[/tex]0[tex]\mu[/tex]r (NI)/(2[tex]\pi[/tex]R) (2[tex]\pi[/tex]R)(4h)
= [tex]\mu[/tex]0[tex]\mu[/tex]rNI(4h)
Plugging in [tex]\mu[/tex]r = 8000, I = 50 x 10-3, N = 500, h = 20 x 10-3 gives [tex]\Phi[/tex]=0.0201Wb

Is this right? If not, where did I go wrong, how do I fix it?

b) Um = (1/2)(50 x 10-3)(0.0201) = 5.03 x 10-4 J

Again, is this right? I'm not comfortable with this course at all. If it's incorrect, how do I fix it? What do I do?

Thanks in advance.
 
Last edited:
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  • #2


Hello,

Your calculations for both parts are correct! Great job!

For part a), you used the correct formula for magnetic flux and correctly substituted in the values for the variables. You also correctly used the formula for magnetic flux density (B) and substituted in the values for relative permeability, current, number of turns, and height. This gave you the correct answer for magnetic flux (0.0201 Wb).

For part b), you used the formula for magnetic energy and correctly substituted in the values for current and magnetic flux. This gave you the correct answer for magnetic energy (5.03 x 10^-4 J).

Keep up the good work! Just make sure to double check your calculations and units when solving problems like this.


 

1. What is magnetostatics?

Magnetostatics is a branch of electromagnetism that deals with the study of static magnetic fields and their effects on charged particles. It is concerned with the behavior of electrically charged objects in motion and the resulting magnetic fields.

2. What is magnetic flux?

Magnetic flux is a measure of the strength of a magnetic field passing through a given area. It is represented by the symbol Φ and is measured in units of webers (Wb). It is calculated by multiplying the magnetic field strength by the area that it passes through, with the direction of the magnetic field perpendicular to the area.

3. What is an inductor?

An inductor is a passive electronic component that stores energy in the form of a magnetic field. It is typically made of a coil of wire and is used in electronic circuits to control the flow of current. Inductors are commonly used in power supplies, filters, and signal processing circuits.

4. What is a toroidal inductor?

A toroidal inductor is a type of inductor that is shaped like a doughnut or torus. It consists of a coil of wire wound around a ferrite or iron core in a circular shape. Toroidal inductors have a number of advantages over other types of inductors, including low electromagnetic interference and high inductance.

5. How is energy stored in a toroidal inductor?

Energy is stored in a toroidal inductor in the form of a magnetic field. When a current flows through the coil, a magnetic field is created in the core. This magnetic field stores energy, which can be released when the current is disrupted. The amount of energy stored in a toroidal inductor is proportional to the square of the current and the number of turns in the coil.

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