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A uniform field H = -600 uy A/m exist in free space. The total energy stored in spherical region 1 cm in radius centered at the origin in free space is
- a)0.226 J/m3
- b)1.452 J/m3
- c)1.68 J/m3
- d)0.84 J/m3
Correct answer is option 'A'. Can you explain this answer?
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Calculation of Energy Stored in Spherical Region
- Given field strength: H = -600 u A/m
- Radius of spherical region: r = 1 cm = 0.01 m
- Energy density formula: u = 0.5 * H^2 / μ
Calculating Energy Density
- Given permeability of free space: μ = 4π * 10^-7 H/m
- Substitute the values in the formula:
u = 0.5 * (-600)^2 / (4π * 10^-7)
u = 0.5 * 360000 / (4π * 10^-7)
u = 180000 / (4π * 10^-7)
u ≈ 3.59 * 10^11 J/m^3
Calculating Total Energy Stored
- Total energy stored in the spherical region:
E = u * V
V = (4/3) * π * r^3
V = (4/3) * π * (0.01)^3
V ≈ 4.19 * 10^-7 m^3
E = 3.59 * 10^11 * 4.19 * 10^-7
E ≈ 0.226 J
Therefore, the total energy stored in the spherical region of 1 cm radius centered at the origin in free space is approximately 0.226 J/m^3, which corresponds to option 'A'.
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A uniform field H = -600 uyA/m exist in free space. The total energy stored in spherical region 1 cm in radius centered at the origin in free space isa)0.226 J/m3b)1.452 J/m3c)1.68 J/m3d)0.84 J/m3Correct answer is option 'A'. Can you explain this answer?
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