Magnetic Potential Energy

📊 advanced

$$U = -\vec{m} \cdot \vec{B} = -mB \cos \theta$$

The energy of a magnetic dipole (like a compass needle) in an external magnetic field.

Variables & Units

$m$

Magnetic dipole moment

Unit: $A \cdot m^2$ or $J/T$

$B$

Magnetic field

Unit: Tesla ($T$)

$\theta$

Angle between $m$ and $B$

Unit: Degrees

Key Information

📐 Derived From

Work done to rotate the dipole in the field.

💡 Example

Energy of a proton spin in an MRI scanner.

🔧 Applications

Atomic physics, compass design, and NMR spectroscopy.

⚠️ Constraints

Uniform magnetic field.

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