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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)0.08 H
Correct answer is option '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...
Given:
Length of smaller solenoid, l1 = 20 cm = 0.2 m
Area of cross-section of smaller solenoid, A1 = 4 cm² = 4 × 10^-4 m²
Number of turns of smaller solenoid, N1 = 4000
Length of larger solenoid, l2 = 10 cm = 0.1 m
Area of cross-section of larger solenoid, A2 = 8 cm² = 8 × 10^-4 m²
Number of turns of larger solenoid, N2 = 2000
Formula used:
Mutual inductance of two solenoids, M = μ0 × N1 × N2 × A1 × A2 / (l1 + l2)
where μ0 = 4π × 10^-7 T m/A is the permeability of free space.
Calculation:
M = μ0 × N1 × N2 × A1 × A2 / (l1 + l2)
= 4π × 10^-7 × 4000 × 2000 × 4 × 10^-4 × 8 × 10^-4 / (0.2 + 0.1) = 0.02 H
Therefore, the mutual inductance of the system is 0.02 H.
Length of smaller solenoid, l1 = 20 cm = 0.2 m
Area of cross-section of smaller solenoid, A1 = 4 cm² = 4 × 10^-4 m²
Number of turns of smaller solenoid, N1 = 4000
Length of larger solenoid, l2 = 10 cm = 0.1 m
Area of cross-section of larger solenoid, A2 = 8 cm² = 8 × 10^-4 m²
Number of turns of larger solenoid, N2 = 2000
Formula used:
Mutual inductance of two solenoids, M = μ0 × N1 × N2 × A1 × A2 / (l1 + l2)
where μ0 = 4π × 10^-7 T m/A is the permeability of free space.
Calculation:
M = μ0 × N1 × N2 × A1 × A2 / (l1 + l2)
= 4π × 10^-7 × 4000 × 2000 × 4 × 10^-4 × 8 × 10^-4 / (0.2 + 0.1) = 0.02 H
Therefore, the mutual inductance of the system is 0.02 H.
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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 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)0.08 HCorrect answer is option 'A'. Can you explain this answer?
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