Magnetic fields store energy when electric current flows through a conductor. This energy is crucial in various applications, from power lines to electromagnets. Understanding how magnetic fields store and transfer energy is key to grasping their role in electrical systems.
The energy stored in magnetic fields can be quantified using formulas that relate to field strength and volume. This concept extends to inductors, where the energy storage depends on inductance and current. These principles underpin the functioning of transformers and electromagnets in our everyday lives.
Energy in Magnetic Fields
Energy storage in magnetic fields
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Magnetic fields store energy when an electric current flows through a conductor
Energy is stored in the space surrounding the conductor (power lines, electromagnets)
formula:
uB=2μ0B2
uB represents in J/m³
B represents magnetic field strength in teslas (T)
μ0 represents , equal to 4π×10−7 T⋅m/A
Total energy stored in a magnetic field calculated by volume integral of energy density:
UB=∫uBdV=∫2μ0B2dV
UB represents total energy stored in the magnetic field in joules (J)
dV represents differential volume element in m³
Equation for inductor energy
is a passive electrical component that stores energy in its magnetic field when electric current flows through it (, )
Magnetic field strength inside an is proportional to the current:
B=μ0nI
n represents number of turns per unit length of the inductor in turns/m
I represents current flowing through the inductor in amperes (A)
Substituting magnetic field strength expression into energy density formula:
uB=2μ0(μ0nI)2=2μ0n2I2
Total energy stored in an inductor calculated by volume integral of energy density:
UL=∫2μ0n2I2dV=2μ0n2I2∫dV=2μ0n2I2Al=2LI2
A represents cross-sectional area of the inductor in m²
l represents length of the inductor in m
L=μ0n2Al represents inductance of the inductor in (H)
Applications of magnetic energy storage
Electromagnets
Consist of a coil of wire wrapped around a (iron, steel)
Electric current flowing through the coil generates a magnetic field
Magnetic field strength depends on the current and number of turns in the coil
Stored magnetic energy used to perform work (lifting heavy objects, trains)
Transformers
Consist of two or more coils of wire wound around a common ferromagnetic core
Alternating current in the primary coil creates a changing magnetic field in the core
Changing magnetic field induces an alternating voltage in the secondary coil
Voltage transformation ratio determined by the ratio of the number of turns in the primary and secondary coils
Energy transferred from the primary to the secondary coil through the shared magnetic field in the core
Used to step up or step down voltages in power transmission and distribution systems (, electronic devices)
Magnetic properties of materials
Magnetic flux: The total magnetic field passing through a given area
Magnetic dipole moment: A measure of the torque experienced by a magnetic dipole in an external magnetic field
: A measure of how easily a material can be magnetized in response to an external magnetic field
: The process by which materials form magnetic dipoles when exposed to a magnetic field
: A measure of a material's ability to support the formation of a magnetic field within itself