Question

The magnitude of the magnetic induction at a point on the axis at a large distance (r) from the centre of a circular coil of 'n' turns and area 'A' carrying current (l) is given by ______.

विकल्प

• `"B"_"axis" = mu_0/(4pi) * "nA"/"Ir"^3`

• `"B"_"axis" = mu_0/(4pi) * (2"nlA")/"r"^3`

• `"B"_"axis" = mu_0/(4pi) * (2"nl")/"Ar"^3`

• `"B"_"axis" = mu_0/(4pi) * ("nlA")/"r"^3`

Answer 1

The magnitude of the magnetic induction at a point on the axis at a large distance (r) from the centre of a circular coil of 'n' turns and area 'A' carrying current (l) is given by `underlinebb("B"_"axis" = mu_0/(4pi) * (2"nlA")/"r"^3)`.

Explanation:

As we know that the magnetic field on the axis of a circular current carrying loop,

B = `(mu_0"nla"^2)/(2 ("r"^2 + "a"^2)^(3//2))`   ...(i)

where, I = current through the coil,

a = radius of a circular loop,

r = distance of point from the centre along the axis and

n = number of turns in the coil.

Area of the coil, A = πa²

`=> "a"^2 = "A"/pi`   ...(ii)

and it r >> a then, (r² + a²)^3/2 = r³    ...(iii)

From Eqs. (i), (ii) and (iii), we get

B = `((mu_0"nl")/"2r"^3) "A"/pi xx 2/2`

`=> "B" = (2mu_0 "nlA")/(4pi"r"^3)`