Amount of energy stored in a magnetic field

In summary, an air-core solenoid with 57 turns, length of 4.96 cm, and diameter of 1.46 cm has a magnetic field energy of 2.7355 μJ when carrying a current of 0.634 A. This was calculated using the formula U = (1/2) Induction (I ^2), where Induction was first calculated to be 1.3785e-5 using the formula Induction = 4πe-7 (N^2/L)A. The correct equation to calculate energy stored in a solenoid is U = (1/2) Induction (I ^2), as explained in the provided website.
  • #1
rinarez7
27
0
1. An air-core solenoid with 57 turns is 4.96 cm
long and has a diameter of 1.46 cm.
The permitivity of free space is 4×10−7 T·
m/A.
How much energy is stored in its magnetic
field when it carries a current of 0.634 A ?
Answer in units of μJ.
2.
B = mu-o (I) (N)/ L
Induction= mu-0 (N^2/l) A
U= (1/2) Induction (I ^2)

3. First I calculated Induction= 4pie-7 ( 57turns ^2/ .0496m) (pi(.0146^2))= 1.3785e-5

Then I used U = (1/2) induction (0.634 A ^2)= 2.7355μJ

I am on the wrong path? I thought of calculating the magentic field as well
using my first eqaution= 9.09795 e-4 T but I couldn't find the correct eqaution/ relationship to calculate the energy stored. Thanks in advance for any help!
 
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What is the amount of energy stored in a magnetic field?

The amount of energy stored in a magnetic field is determined by the strength of the magnetic field and the volume of the space that it occupies. It can be calculated using the equation E = 1/2 * B^2 * V, where B is the magnetic field strength and V is the volume.

How is the amount of energy stored in a magnetic field measured?

The amount of energy stored in a magnetic field is measured in joules (J) or ergs (erg). It can also be measured in units of magnetic flux density (teslas) squared multiplied by volume (cubic meters).

Can the amount of energy stored in a magnetic field be changed?

Yes, the amount of energy stored in a magnetic field can be changed by altering the strength of the magnetic field or by changing the volume of the space it occupies. It can also be changed by introducing materials with different magnetic properties into the field.

What are some real-life applications of the amount of energy stored in a magnetic field?

The amount of energy stored in a magnetic field has many practical applications, including in generators, motors, transformers, and magnetic storage devices such as hard drives. It is also used in magnetic levitation technology, where the energy stored in a magnetic field is used to lift and suspend objects.

How does the amount of energy stored in a magnetic field relate to electromagnetic waves?

Electromagnetic waves are a form of energy that can be produced by changing the amount of energy stored in a magnetic field. When an electric current is passed through a wire, it creates a magnetic field, and when the current is changed, it creates a changing magnetic field, which in turn produces an electromagnetic wave.

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