A $2 m$ long solenoid having diameter $6 c m$ and $2000$ turns has a secondary of $500$ turns wound closely near its mid-point. Calculate the mutual inductance between the two coils.

Open in App

Solution

Length of the solenoid $L = 2$ m
Radius of the solenoid $r = \frac{6}{2} = 3$ cm
Area of the solenoid $A = π r^{2}$
$∴$ $A = π \times (0.03)^{2} = 0.0028$ $m^{2}$
Number of turns in solenoid $N_{s} = 2000$
Number of turns in coil $N_{c} = 500$
Mutual inductance between the coils $M = \frac{μ_{o} N_{s} N_{c} A}{L}$
$∴$ $M = \frac{4 π \times 10^{- 7} \times 2000 \times 500 \times 0.0028}{2}$
$⟹$ $M = 1.76 \times 10^{- 3}$ $H = 1.76 m H$

Suggest Corrections

Similar questions

Q. A 2 m long solenoid with diameter 2 cm an 2000 turns has a secondary coil of 1000 turns wound closely near its midpoint. The mutual inductance between the two coils is

The current in a long solenoid of radius R and having n turns per unit length is given $i = i_{0} sin ω t .$ A coil having N turns is wound around it near the centre. Find (a) the induced emf in the coil and (b) the mutual inductance between the solenoid and the coil.

Q. A long solenoid of length

L

, cross section

A

having

N_{1}

turns has wound about its centre with a small coil of

N_{2}

turns as shown in Fig. The mutual inductance of two circuits is:

Q. A coil of

100

turns and having radius

1 cm

is kept co-axially within a long solenoid of

8

turns per

cm

with radius

5 cm .

Find the mutual inductance between the coil and solenoid-

A solenoid coil has 10 turns per cm along its length and a cross sectional area of 10 cm². 100 turns of another wire are wound round the first solenoid coaxially. The two coils are electrically insulated from each other. The mutual inductance between the two coils is

Join BYJU'S Learning Program

A 2m long solenoid having diameter 6cm and 2000 turns has a secondary of 500 turns wound closely near its mid-point. Calculate the mutual inductance between the two coils.

Length of the solenoid L=2 mRadius of the solenoid r=62=3 cmArea of the solenoid A=πr2∴ A=π×(0.03)2=0.0028 m2Number of turns in solenoid Ns=2000Number of turns in coil Nc=500Mutual inductance between the coils M=μoNsNcAL∴ M=4π×10−7×2000×500×0.00282⟹ M=1.76×10−3 H=1.76mH

A $2 m$ long solenoid having diameter $6 c m$ and $2000$ turns has a secondary of $500$ turns wound closely near its mid-point. Calculate the mutual inductance between the two coils.