Question

Two long, thin parallel wires are placed 12.0 cm apart, as shown below.

Each wire carries a 28 A current, but the currents are flowing in opposite directions.

Determine the magnetic field vector at the point P, which is 10.4 cm from one wire, and 6.0 cm from the other.

Please help me find the magnitude and the direction (θ).

Answer 1

given

i₁ = i₂ = 28 A

d₁ = 6 cm

= 0.06 m

d₂ = 10.4 cm

= 0.104 m

B₁ = _o i₁ / 2 d₁

= 4 x 3.14 x 10^-7 x 28 / 2 x 3.14 x 0.06

= 0.00009333 T

B₂ = _o i₂ / 2 d₂

= 4 x 3.14 x 10^-7 x 28 / 2 x 3.14 x 0.104

= 0.00005384 T

B = ( 0.00009333² + 0.00005384² )^1/2  

B = 0.0001077 T

θ = tan^-1 ( 0.00005384 / 0.00009333 )

θ = 60^o