Define the term ‘mutual inductance’ between the two coils. Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii r₁ and r₂ (r₂ >> r₁). Total number of turns in the two solenoids is N₁and N₂ respectively.

Solution

The ratio of magnetic flux passing through one coil to the current passing through the other is known as mutual inductance between the two coils.

Consider current I₂ flowing through the outer coil.

Magnetic field due to current I₂ is given by, $straight mu subscript straight o space straight N subscript 2 over straight i space straight x space straight I subscript 2$

Therefore, resultant magnetic flux linked with the inner coil is,
$straight ϕ subscript 12 space equals space straight N subscript 1 space. space open parentheses straight mu subscript straight o straight N subscript 2 over straight i straight x space straight l subscript 2 close parentheses straight x space πr subscript 1 squared space space space space space space space equals space open parentheses straight mu subscript straight o space fraction numerator straight N subscript 1 straight N subscript 2 over denominator straight i end fraction. space πr subscript 1 squared close parentheses straight l subscript 2 Therefore comma space straight M subscript 12 space equals space straight mu subscript straight o space fraction numerator straight N subscript 1 straight N subscript 2 over denominator straight i end fraction space. space space πr subscript 1 squared$

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Electric Charges And Fields

Define the term ‘mutual inductance’ between the two coils. Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii r₁ and r₂ (r₂ >> r₁). Total number of turns in the two solenoids is N₁and N₂ respectively.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

Define the term ‘mutual inductance’ between the two coils. Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii r1 and r2 (r2 >> r1). Total number of turns in the two solenoids is N1 and N2 respectively.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Define the term ‘mutual inductance’ between the two coils. Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii r₁ and r₂ (r₂ >> r₁). Total number of turns in the two solenoids is N₁and N₂ respectively.

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?