## Energy in a Magnetic Field

10.3 Energy in a Magnetic Field

### Learning Objectives

By the end of this section, you will be able to:

- Explain how energy can be stored in a magnetic field
- Derive the equation for energy stored in a coaxial cable given the magnetic energy density

### Energy Stored in a Magnetic Field

**Practice!**

Practice 10.3.1 |
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A solenoidal inductor for a printed circuit board is being redesigned. To save weight, the number of turns is reduced by one-half, with the geometric dimensions kept the same. By how much must the current be changed if the energy stored in the inductor is to remain the same? |

**Discuss!**

Recall the formulas for energy density:

and

How does the energy density of a 1.0-T magnetic field compare with the energy density of a 1.0-V/m electric field?

An air-core solenoid with 50 turns is 7.95 cm long and has a diameter of 1.85 m. How much energy is stored in its magnetic field when it carries a current of 0.505 A?