To determine The rank of the solenoids in decreasing order of magnetic energy stored. Explanation The number of turns per unit length of the solenoid is same for all the solenoids. Write the formula for the energy per unit volume stored in magnetic field. u B = B 2 2 μ 0 Here, u B is the energy density, B is the magnetic field, μ 0 is the permeability of the free space. Re-write the above equation by substituting the expression for the magnetic field of solenoid. u B = ( μ 0 n I ) 2 2 μ 0 Here, n is the number of turns per unit length, I is the current. Write the formula for the energy stored in solenoid. U B = ( μ 0 n I ) 2 V 2 μ 0 Here, U B is the energy stored in the solenoid, V is the volume. Re-write the above equation by substituting the expression for the volume of the solenoid. U B = ( μ 0 n I ) 2 π ( d 2 / 4 ) L 2 μ 0 Here, d is the diameter of the solenoid, L is the length of the solenoid. Re-write the above equation to see the dependence of the energy stored on various parameters. U B ∝ I 2 d 2 L (I) Conclusion: Substitute 6 cm for L , 1 cm for d , 150 mA for I in equation for option(a). U B ∝ ( 150 mA ) 2 ( 1 cm ) 2 ( 6 cm ) ∝ 135000 mA ⋅ cm 3 Substitute 12 cm for L , 0

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ISBN: 9781260486919

Author: GIAMBATTISTA

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Chapter 20.9, Problem 20.9CP

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The rank of the solenoids in decreasing order of magnetic energy stored.

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