A short solenoid of length 4 cm , radius 2 cm and 100 turns is placed inside and on the axis of a long solenoid of length 80 cm and 1500 turns. A current of 3 A flows through the short solenoid. The mutual inductance of two solenoids is:

Question

A short solenoid of length 4 cm , radius 2 cm and 100 turns is placed inside and on the axis of a long solenoid of length 80 cm and 1500 turns. A current of 3 A flows through the short solenoid. The mutual inductance of two solenoids is: (A)  2.96× 10-4H  (B)  5.3× 10-5H  (C)  3.52× 10-3H  (D)  8.3× 10-5H

Tardigrade Admin · Accepted Answer

M21=(μ 0N1N2A2/l1) ∴ M21=( beginalign (4× 3.14× 10-7)× 1500× 100 × 3.14(2× 10-2)2 endalign/80× 10-2) M21=2.96× 10-4H ⇒ M21=M21=2.96× 10-4H

Q. A short solenoid of length $4 c m$ , radius $2 c m$ and $100$ turns is placed inside and on the axis of a long solenoid of length $80 c m$ and $1500$ turns. A current of $3 A$ flows through the short solenoid. The mutual inductance of two solenoids is:

$2.96 \times 10^{- 4} H$

$5.3 \times 10^{- 5} H$

$3.52 \times 10^{- 3} H$

$8.3 \times 10^{- 5} H$

$2.96 \times 10^{- 3} H$

$M_{21} = \frac{μ _{0} N _{1} N _{2} A _{2}}{l _{1}}$
$∴$ $M_{21} = \frac{( 4 \times 3.14 \times 10 ^{- 7} ) \times 1500 \times 100 \times { 3.14 ( 2 \times 10 ^{- 2} ) ^{2} }}{80 \times 10 ^{- 2}}$
$M_{21} = 2.96 \times 10^{- 4} H$
$\Rightarrow$ $M_{21} = M_{21} = 2.96 \times 10^{- 4} H$

Q. A short solenoid of length 4cm , radius 2cm and 100 turns is placed inside and on the axis of a long solenoid of length 80cm and 1500 turns. A current of 3A flows through the short solenoid. The mutual inductance of two solenoids is:

2.96×10−4H

5.3×10−5H

3.52×10−3H

8.3×10−5H

2.96×10−3H

M21​=l1​μ0​N1​N2​A2​​ ∴ M21​=80×10−2​(4×3.14×10−7)×1500×100×{3.14(2×10−2)2}​​ M21​=2.96×10−4H ⇒ M21​=M21​=2.96×10−4H