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Question: A solenoid of length 30 cm with 10 turns per centimetre and area of cross-section 40 cm2 completely ...

A solenoid of length 30 cm with 10 turns per centimetre and area of cross-section 40 cm2 completely surrounds another co-axial solenoid of same length, area of cross-section 20 cm2 with 40 turns per centimetre. The mutual inductance of the system is

A

10 H

B

8 H

C

3 mH

D

30 mH

Answer

3 mH

Explanation

Solution

Mutual induction of the system where A2\mathrm { A } _ { 2 } is the area of inner solenoid.

n1=10 cm−1=1000 m−1\mathrm { n } _ { 1 } = 10 \mathrm {~cm} ^ { - 1 } = 1000 \mathrm {~m} ^ { - 1 }

n2=40 cm−1=4000 m−1\mathrm { n } _ { 2 } = 40 \mathrm {~cm} ^ { - 1 } = 4000 \mathrm {~m} ^ { - 1 }

1=30 cm=30×10−2 m1 = 30 \mathrm {~cm} = 30 \times 10 ^ { - 2 } \mathrm {~m}

A2=20 cm2=20×10−4 m2A _ { 2 } = 20 \mathrm {~cm} ^ { 2 } = 20 \times 10 ^ { - 4 } \mathrm {~m} ^ { 2 }

∴M=4π×10−7×1000×4000×20×10−4×30×10−2\therefore \mathrm { M } = 4 \pi \times 10 ^ { - 7 } \times 1000 \times 4000 \times 20 \times 10 ^ { - 4 } \times 30 \times 10 ^ { - 2 } =301.44×10−5H=3mH= 301.44 \times 10 ^ { - 5 } \mathrm { H } = 3 \mathrm { mH }