Question

It is proposed to store 1.00kW?h=3.60

Answer 1

given that ::

electrical energy, E = 3.6 x 10⁶ J

magnetic field, B = 0.6 T

Part-A :

magnetic density per unit volume is given as,

U / V = B² / 2 ₀                       { eq. 1 }

or V = 2 ₀ U / B²

where, U = E = 3.6 x 10⁶ J

₀ = permeability constant = 4 x 10^-7 N/A²

inserting the values in above eq,

V = 2 (4 x 10^-7 N/A²) (3.6 x 10⁶ J ) / (0.6 T)²

V = (8 x 3.6 x 10^-1) / (0.36)

V = 8 = 8 X 3.14

V = 25.1 m³

Part-B :

If instead this amount of energy is to be stored in a volume which is equivalent to a cube, then magnetic field is given as :

using eq.1,                U / V = B² / 2 ₀           

B = 2 ₀ U / V                  { eq.2 }

where, V = volume of the cube = (side)³

V = (0.35 m)³ = 0.042875 m³

inserting the values in eq.2,

B = 2 (4 x 10^-7 N/A²) (3.6 x 10⁶ J) / (0.042875 m³)

B = (8 x 3.14 x 3.6 x 10^-1) / (0.042875 m³)

B = 90.432 x 10^-1 / 0.042875 T

B = 210.92 T

B = 14.5 T