Two long, parallel wires are separated by a distance of 0.4 m. The currents l_1

Question

Two long, parallel wires are separated by a distance of 0.4 m. The currents l_1 = 8 A and I_2 = 5 A have the directions shown. a) Calculate the total (net) magnetic field created by the two currents at a distance 0.1 m below the bottom wire. What is the direction of the net magnetic field at 0.1 m below the bottom wire? I. Into the page Il Out of the page III To the right IV. To the left Find the force per unit length acting on the top wire. At what distance below the bottom wire is the magnetic field created by the top current equal to the magnetic field created by the bottom current?

Explanation / Answer

(A) Magntic field due to current carrying wire,

B = u0 I / (2 pi r)

at 0.1 m below bottom wire,

B = B2 - B1

= (u0 I2 / (2 pi (0.1))) - (u0 I1 / (2 pi (0.5)))

= (4pi x 10^-7 / 2pi) [ 5/ 0.1 - 8 / 0.5]

= 6.8 x 10^-6 T ........Ans

Direction: (ii) out of the page .........Ans

Force per unit length, F/L = u0 I1 I2 / (2 pi r)

= (4pi x 10^-7 x 8 x 5) / (2 x pi x 0.4)

= 2 x 10^-5 N/m ..........Ans

suppose at distance d below the bottom wire,

B = (u0 I2 / (2 pi d)) - (u0 I1 / (2 pi (d + 0.4))) = 0

5 / d - 8 /(d + 0.4) = 0

5d + 2 = 8 d

d = 0.67 m ........Ans

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