Two long parallel conductors separated by 140 cm carry curre

Two long, parallel conductors, separated by 14.0 cm, carry currents in the same direction. The first wire carries a current I₁ = 3.00 A, and the second carries I₂ = 8.00 A. (See figure below. Assume the conductors lie in the plane of the page.)

(a) What is the magnetic field created by I₁ at the location of I₂?

Magnitude (T)=

Direction=

(b) What is the force per unit length exerted by I₁ on I₂?

Magnitdue (N/m)=

Direction=

(c) What is the magnetic field created by I₂ at the location of I₁?

Magnitude (N/m)=

Direciton=

(d) What is the force per length exerted by I₂ on I₁?

Magnitude (N/m)=

Direction=

Solution

B₁ = mu₀ I₁ / 2 pi r

= (4 pi * 10^-7 * 3.00 ) / (2 pi * 14 * 10^-2) = 4.29 mu T

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force per unit length = mu₀ I₁ I₂ / 2 pi r

= (4 pi * 10-7 * 3.00 * 8.00) / (2 pi * 14 * 10^-2) = 0.0000343 N = 34.3 muN

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B₂ = mu₀ I₂ / 2 pi r

= (4 pi * 10-7 * 8.00 ) / (2 pi * 14 cm) = 11.4 muT

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force per unit length = mu₀ I₁ I₂ / 2 pi r

= (4 pi * 10-7 * 3.00 * 8.00) / (2 pi * 14 * 10^-2)

= 0.0000343 N = 34.3 muN