Physics, asked by rinkalvakani12, 6 months ago

Apply Ampere 'a circuital law to calculate magnetic field inside a long solenoid ​

Answers

Answered by itzqueen90
2

Explanation:

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

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