#### Question

Derive an expression for self inductance of a long solenoid of length *l*, cross-sectional area A having N number of turns.

#### Solution

Magnetic field *B* inside a solenoid carrying a current *i* is . `mu_0 ni`

*B* =`mu_0ni`

Let *n* be the number of turns per unit length.

`Nphi_B = nlBA`

Where,

*N* is total number of turns

*l* is the length of the solenoid

Inductance, `L = (Nphi_B)/i`

Substituting, we obtain

`L = (nlBA)/i`

Substituting the value of *B*, we obtain

`L = (nLmu_0niA)/i`

`L = n^2lmu_0A`

Inductance *L* of a solenoid is:

`L =mu_0n^2lA`

Is there an error in this question or solution?

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Derive an Expression for Self Inductance of a Long Solenoid of Length L, Cross-sectional Area a Having N Number of Turns. Concept: Inductance - Self-Inductance.

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