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Energy density in Magnetic fields
Let's figure out how much energy a magnetic field has per unit volume!
Created by Vibhor Pandey.
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Cool, how exactly does energy exist in a vacuum? And why?(2 votes)
The energy in a solenoid or inductor in a vacuum is stored in the magnetic field that is created when current flows through the solenoid. This magnetic field represents potential energy because it can do work on a charged particle that enters the field.
The energy stored in a solenoid can be expressed in terms of the magnetic field (B), the cross-sectional area (A), and the length (l) of the solenoid. The expression for the magnetic energy stored in a solenoid is given by:
U = (μ₀B²Al)/2
where:
- U is the energy stored,
- μ₀ is the permeability of free space,
- B is the magnetic field,
- A is the cross-sectional area, and
- l is the length of the solenoid.
This equation tells us that the energy stored in a solenoid is directly proportional to the square of the magnetic field, the cross-sectional area, and the length of the solenoid. This means that increasing any of these parameters will increase the amount of energy stored.
The reason why energy can exist in a vacuum in this context is because a vacuum can support electric and magnetic fields. Even though a vacuum is devoid of matter, it's not devoid of physical properties. It can carry light, which is an electromagnetic wave, and so it can also carry magnetic fields, which are part of electromagnetic waves. Therefore, when current flows through a solenoid in a vacuum, it creates a magnetic field that stores energy.
Hope this helps!!(2 votes)