Question

A state ampere law and hence obtain an expression for the magenetic induction at any point neat astraight concentration carrying a current​

Answer 1

Answer:

Ampere's circuital law states that line integral of magnetic field around any closed loop is equal to μo 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   ∮loopB.dl=∫Bab.L+∫Bbc.L′+∫Bcd.L+∫Bda.L′

The value of first term   ∫Bab.L=BL

The second and fourth term are zero because angle between magnetic field and the length loop is 90o.

The third term is also zero as the value of magnetic field outside the solenoid is zero.

Total current flowing through the loop   Itotal=(nL)I

From Ampere's circuital law, we get    BL=μo(nLI) 

⟹   B=μonI