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

Question

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

Tardigrade Admin · Accepted Answer

Mutual inductance of the system, M=μ0n1n2A2l where A2 is the area of inner solenoid n1=10 cm-1=1000 m-1 n2=40 cm-1=4000 m-1 l=30 cm=30× 10-2 m A2=20 cm2=20× 10-4 m2 ∴ M=4π ×10-7×1000×4000×20×10-4×30×10-2 =301.44×10-5 H=3 mH

Q. A solenoid of length $30 c m$ with $10$ turns per centimetre and area of cross-section $40 c m^{2}$ completely surrounds another co-axial solenoid of same length, area of cross-section $20 c m^{2}$ with $40$ turns per centimetre. The mutual inductance of the system is

$10 H$

$8 H$

$3 m H$

$30 m H$

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

10H

8H

3mH

30mH

Mutual inductance of the system, M=μ0​n1​n2​A2​l where A2​ is the area of inner solenoid n1​=10cm−1=1000m−1 n2​=40cm−1=4000m−1 l=30cm=30×10−2m A2​=20cm2=20×10−4m2 ∴M=4π×10−7×1000×4000×20×10−4×30×10−2 =301.44×10−5H=3mH

Q. A solenoid of length $30 c m$ with $10$ turns per centimetre and area of cross-section $40 c m^{2}$ completely surrounds another co-axial solenoid of same length, area of cross-section $20 c m^{2}$ with $40$ turns per centimetre. The mutual inductance of the system is

$10 H$

$8 H$

$3 m H$

$30 m H$