Magnetic Field within the solenoid

What is Solenoid?

A solenoid as a long coil of wire tightly bound in the helical form . If the turns are closely spaced, the resultant magnetic field inside the solenoid becomes Fairly uniform.

Magnetic Field within the solenoid

∮▒〖¯B.dl 〗=μ_0 i by amperes law

∫_a^b▒〖¯B.¯dl〗+ ∫_b^c▒〖¯B.¯dl〗+ ∫_c^d▒〖¯B.¯dl〗+∫_d^a▒〖¯B.¯dl〗=μ_0 i
for path b→c & d→a   ¯B⊥¯dl∴ ∫_b^c▒〖¯B.dl〗=0 ,∫_d^a▒〖¯B.¯dl〗=0
For path c→d   B=0  ∫_c^d▒〖¯B.¯dl〗=0
∫_a^b▒〖¯B.¯dl〗=Bl
Bl =μ_0  NI
B=(μ_0 NI)/l     n=N/l
n→no.if turns per unit length
B=μ_0 nI

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