Drive expression of M.F. Is a solenoid carrying current I & number of turn per unit length are n
Answers
Answer:
Ampere's circuital law states that line integral of magnetic field around any closed loop is equal to μ
o
times the electric current flowing through the cross-section area enclosed by that loop.
Mathematically, ∮B.dl=μI
Let the current flowing in the solenoid having number of turns per unit length n be I.
Magnitude of magnetic field inside the solenoid is B while at outside is zero.
Now ∮
loop
B.dl=∫B
ab
.L+∫B
bc
.L
′
+∫B
cd
.L+∫B
da
.L
′
The value of first term ∫B
ab
.L=BL
The second and fourth term are zero because angle between magnetic field and the length loop is 90
o
.
The third term is also zero as the value of magnetic field outside the solenoid is zero.
Total current flowing through the loop I
total
=(nL)I
From Ampere's circuital law, we get BL=μ
o
(nLI)
⟹ B=μ
o
nI
Answer:
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