Energy Stored in Magnetic Field of Solenoid

In summary, the magnetic field inside an air-filled solenoid is 0.800T, and using the equation U=(1/2)(B^2)(area*length)/(u), the energy stored in this field is approximately 45.324 J. One should double check the value used for permeability when using this equation.
  • #1
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Homework Statement


The magnetic field inside an air-filled solenoid 39.9cm long and 2.00cm in diameter is 0.800T. Approximately how much energy is stored in this field?


Homework Equations



U=(1/2)LI^2
=> U = (1/2)(B^2)(area*length)/(u)

The Attempt at a Solution


I discovered how to derive the bottom equation from the top equation from http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/indeng.html#c2

The derivation on the site seems to make sense, but when I try to use the bottom equation I get:
U = (1/2)(0.8^2)(Pi*0.01^2)*(0.399)/(8.85*10^-7) = 45.324 J

What am I missing here?

Thanks,
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  • #2
Check the value you use for permeability.
 
  • #3
Kurdt said:
Check the value you use for permeability.

Oh wow do I feel stupid now... Thanks for the help!
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1. What is a solenoid?

A solenoid is a coil of wire that carries an electric current. It often has a cylindrical shape and is used to create a magnetic field.

2. How is energy stored in a solenoid's magnetic field?

When an electric current flows through a solenoid, it creates a magnetic field. This magnetic field stores energy in the form of potential energy, which can be released as kinetic energy when the current is turned off.

3. What factors affect the amount of energy stored in a solenoid's magnetic field?

The amount of energy stored in a solenoid's magnetic field is affected by the number of turns in the coil, the strength of the electric current, and the material of the core (if any). Increasing any of these factors will increase the energy stored in the magnetic field.

4. How can the energy stored in a solenoid's magnetic field be calculated?

The energy stored in a solenoid's magnetic field can be calculated using the formula: E = 1/2 * L * I^2, where E is the energy in joules, L is the inductance of the solenoid in henries, and I is the current in amperes.

5. How is the energy stored in a solenoid's magnetic field used in practical applications?

The energy stored in a solenoid's magnetic field is used in a variety of practical applications, such as in electromagnets for lifting heavy objects, in electric motors for converting electrical energy into mechanical energy, and in generators for converting mechanical energy into electrical energy.

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