Amount of energy stored in a magnetic field

In summary, the conversation discusses the calculation of energy stored in the magnetic field of an air-core solenoid with given dimensions and a current of 0.634 A. The equation used is U = (1/2) Induction (I ^2), where Induction is calculated to be 1.3785e-5 using the formula B = mu-o (I) (N)/ L and the given values. The correct value of energy stored is determined to be 2.7355μJ. However, there is a mistake in the calculation of inductance where the diameter was used instead of the radius. Upon correcting this, the same result is obtained.
  • #1
rinarez7
27
0
1. 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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  • #2
0.0146 is the diameter, not the radius.
 
  • #3
My mistake, I did use the diameter/ 2 in my calculations ( just translated it incorrectly) so I still had the same calculation. Is there something else I am missing?
 
  • #4
Check the calculation of inductance.
 

FAQ: Amount of energy stored in a magnetic field

What is magnetic energy?

Magnetic energy is the energy stored in a magnetic field. It is the result of the movement of electrically charged particles, such as electrons, within the magnetic field.

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

The amount of energy stored in a magnetic field can be calculated by multiplying the magnetic field strength (in teslas) by the square of the distance between the magnetic poles (in meters) and dividing by two. The formula is E = (B^2 * d^2) / 2, where E is the energy stored, B is the magnetic field strength, and d is the distance between poles.

What factors affect the amount of energy stored in a magnetic field?

The amount of energy stored in a magnetic field is affected by the strength of the magnetic field, the distance between the magnetic poles, and the size and shape of the magnets. It is also affected by any external magnetic fields that may be present.

How is magnetic energy used in everyday life?

Magnetic energy is used in various everyday applications, such as in electric motors, generators, and speakers. It is also used in credit cards, computer hard drives, and MRI machines in the medical field.

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

Yes, the amount of energy stored in a magnetic field can be increased by increasing the strength of the magnetic field or by decreasing the distance between the magnetic poles. This can be achieved by using stronger magnets or by changing the configuration of the magnetic system.

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