Like any field, the Earth's magnetic field stores energy. Find the magnetic energy stored in a space where the strength of the earth's field is 7 ｘ10⁻⁵ T if the space occupies an area of 10 ï½˜10⁸ m² and has a height of 750 m. (Answer: 1.46 ï½˜10⁹ J). 



Data Given:


Magnetic field strength = B = 7 ｘ10⁻⁵ T

Area = A = 10 ｘ10⁸ m²  

Height = h = `\l` = 750 m

µ₀ = 4Ï€ ｘ10⁻⁷ Wb A⁻¹ m⁻¹


To Find:


Magnetic Energy stored in space = `\U_m` = ?


Solution:

The relation for the required Magnetic Energy is


`\U_m` = `\frac {1}{2}` `\frac {B^2}{μ_0}` `\Al`

Putting the corresponding values 


`\U_m` = `\frac {1}{2}` `\frac {(7 ｘ10⁻⁵ T)^2}{4 ｘ 3.1416 ｘ10⁻⁷ Wb A⁻¹ m⁻¹}` ｘ 10 ｘ10⁸ m² ｘ 750 m

`\U_m` = `\frac {1}{2}` ｘ`\frac {49 ｘ10⁻⁻¹⁰ T^2}{12.5664 ｘ10⁻⁷ Wb A⁻¹ m⁻¹}` ｘ 7500 ｘ10⁸ m³

`\U_m` = `\frac {1 ｘ 49 ｘ10⁻¹⁰ T^2 ｘ 7500 ｘ10⁸ m³}{2 ｘ 12.5664 ｘ10⁻⁷ Wb A⁻¹ m⁻¹}`

`\U_m` = `\frac {367500 ｘ10⁻² T^2 m³}{25.1328 ｘ10⁻⁷ Wb A⁻¹ m⁻¹}`

or


`\U_m` = 14622.326 ï½˜10⁵ J

or

`\U_m` = 1462.233 ï½˜10⁶ J

or

`\U_m` = 1.462 ｘ10⁹ J ---------------Ans.




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