The magnitude of magnetic flux density (→B) at a point

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The magnitude of magnetic flux density (^{^→}B) at a point having normal distance d
meters from an infinitely extended wire carrying current of I A is μ₀I (in SI units).
2πd

An infinitely extended wire is laid along the x-axis and is carrying current of 4 A in the +ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying 2 A current in the +ve y direction. μ₀ is permeability of free space. Assume î , ĵ , k̂ to unit vectors along x, y and z axis respectively.

Assuming right handed co-ordinate system, magnetic field intensity, ^{^→}H at coordinate (2, 1, 0) will be

1. 3 k̂ weber / m²
  2π
2. 4 î A / m
  3π
3. 3 k̂ A / m
  2π
4. 0 A/m

Correct Option: C

Magnetic field intensity due to wire carrying 2A current in + Y direction.

H₁ =	I₁	(-k̂) = -	2	k̂ =	1	(-k̂) A / m
	2πd₁		2π2		2π

Magnetic field intensity due to wire carrying 4A current in the + X – direction

H₂ =	I₂	k̂
	2πd₂

H₂ =	4	(k̂) A / m
	2π

Then, resultant field intensity,

H = H₁ + H₂ =	1	(-k̂) +	4	k̂
	2π		2π

H =	3	k̂ A / m
	2π