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A solenoid of length 20 cm area of cross-section 4 cm2 and having 4000 turns is placed inside another solenoid of 2000 turns having a cross-section area 8 cm2 and length 10 cm. The mutual inductance of the system is
  • a)
    0.02 H
  • b)
    0.04 H
  • c)
    0.06 H
  • d)
    0.06 H
Correct answer is 'A'. Can you explain this answer?
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A solenoid of length 20 cm area of cross-section 4 cm2 and having 4000...
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A solenoid of length 20 cm area of cross-section 4 cm2 and having 4000...
The mutual inductance of the system can be calculated using the formula:

M = (μ₀N₁N₂A₁A₂) / d

Where:
M is the mutual inductance
μ₀ is the permeability of free space (4π × 10^-7 Tm/A)
N₁ is the number of turns in the first solenoid (4000 turns)
N₂ is the number of turns in the second solenoid (2000 turns)
A₁ is the cross-sectional area of the first solenoid (4 cm²)
A₂ is the cross-sectional area of the second solenoid (8 cm²)
d is the distance between the two solenoids (length of the second solenoid, 10 cm)

Calculating the mutual inductance:
M = (4π × 10^-7 Tm/A) * (4000 turns) * (2000 turns) * (4 cm²) * (8 cm²) / (10 cm)

Simplifying the equation:
M = (4π × 10^-7 Tm/A) * (4000 turns) * (2000 turns) * (4 cm²) * (8 cm²) / (0.1 m)

Converting the units:
1 cm = 0.01 m
1 cm² = 0.0001 m²

M = (4π × 10^-7 Tm/A) * (4000 turns) * (2000 turns) * (4 * 0.0001 m²) * (8 * 0.0001 m²) / (0.1 m)

M = (4π × 10^-7 Tm/A) * (4000 turns) * (2000 turns) * (0.0004 m²) * (0.0008 m²) / (0.1 m)

M = (4π × 10^-7 Tm/A) * (4000 * 2000) * (0.0004 * 0.0008) / (0.1)

M = (4π × 10^-7 Tm/A) * (8) * (0.00032) / (0.1)

M = (4π × 10^-7 Tm/A) * (0.00256) / (0.1)

M = (4π × 10^-7 Tm/A) * 0.0256

M = 4π × 10^-7 Tm/A * 0.0256

M = 0.0256 * 4π × 10^-7 Tm/A

M = 0.0256 * 4π × 10^-7 H

M ≈ 0.032 H

The correct answer is not 'A' but '0.032 H'.
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Community Answer
A solenoid of length 20 cm area of cross-section 4 cm2 and having 4000...
B=u not n2 I
Flux = B.A.N1=M.I
M=4pi�10^-7�2000/0.1�4000/0.2�4�10^-4
M=6.4pi�10^-3
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A solenoid of length 20 cm area of cross-section 4 cm2 and having 4000 turns is placed inside another solenoid of 2000 turns having a cross-section area 8 cm2 and length 10 cm. The mutual inductance of the system isa)0.02 Hb)0.04 Hc)0.06 Hd)0.06 HCorrect answer is 'A'. Can you explain this answer?
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