How Do You Calculate the Energy Stored in a Magnetic Field?

AI Thread Summary
To calculate the energy stored in a magnetic field, the magnetic energy density can be determined using the formula Ub = (B^2)/(2μ0), yielding a result of 8.1 x 10^6 J/m³. This value represents the energy per unit volume within the magnetic field of the superconducting solenoid. For the total energy stored in the solenoid, the volume must be calculated using the solenoid's dimensions, which involves its length and diameter. The energy stored can then be found by multiplying the energy density by the total volume. Accurate unit representation is crucial for clarity in calculations.
abot
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the problem reads... the magnetic field inside a superconducting solenoid is 4.50T. the solenoid has an inner diammeter of 6.20cm and length 26.0cm.
Determine (a) the magnetic energy density in the field. (b) he enrgy stored in the magnetic field with in the solenoid.

For (a) i use the formula Ub= (B^2)/(2Uo) and i get 8.1x10^6
Is this correct?

For (b) I am not quite sure what to do. I know i must use the length and diameter to find B. or maybe not

I need some guidance.

Thank You
 
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abot said:
For (a) i use the formula Ub= (B^2)/(2Uo) and i get 8.1x10^6
Is this correct?
Yes. (Check your arithmetic.)

For (b) I am not quite sure what to do. I know i must use the length and diameter to find B. or maybe not
Hint: The energy density that you found in (a) is the energy per unit volume.
 
If you had written the units for your first part, the second part would become obvious. Never leave out the units; they are essential.
 
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