Question

Q.6 Determine an expression due to long straight current
carrying wire at a point with the help of Biot-Savert law. ​

Answer 1

Explanation:

Magnetic induction due to infinitely long straight conductor carrying current: XY, is an infinitely long straight conductor carrying a current I(Figure).

P is a point at a distance a from the conductor. AB is a small element of length dl. θ is the angle between the current element Idl and the line joining the element dl and the point P. According to Biot-Savart law, the magnetic induction at the point P due to the current element Idl is.

AC is drawn perpendicular to BP from A.

∠OPA=ϕ, ∠APB=dϕ

In ΔABC, sinθ=

AB

AC

=

dl

AC

∴AC=dlsinθ ..........(2)

From ΔAPC, AC=rdϕ .........(3)

From equations (2) and (3),

rdϕ=dlsinθ ............(4)

Substituting equation (4) in equation (1)

dB=