Question

The earth's magnetic field, like any magnetic field, stores energy. The maximum strength of the earth's field is about 7.0×10⁻⁵T. Find the maximum magnetic energy stored in the space above a city if the space occupies an area of 4.0×10⁸m² and has a height of 1600 m.

Answer 1

The maximum magnetic energy stored in the space above a city is approximately 1.27×10⁷J.

Step-by-step explanation:

To find the maximum magnetic energy stored in the space above a city, we use the formula:

Magnetic Energy = Volume * Magnetic Field Strength² / 2μ₀

Where:

• Volume = Area * Height
• Magnetic Field Strength = 7.0×10⁻⁵T
• μ₀ (mu naught) = 4π×10⁻⁷ T m/A

Plugging in the values, we get:

• Volume = 4.0×10⁸m² * 1600m = 6.4×10¹⁴m³
• Magnetic Field Strength² = (7.0×10⁻⁵T)² = 4.9×10⁻¹⁰T²
• 2μ₀ = 2 * 4π×10⁻⁷ T m/A ≈ 2.51×10⁻⁶T m/A

Substituting these values back into the formula, we can calculate the maximum magnetic energy stored:

Magnetic Energy = (6.4×10¹⁴m³) * (4.9×10⁻¹⁰T²) / (2.51×10⁻⁶T m/A) = 1.27×10⁷J