Two long, parallel conductors separated by 10.0 cm carry currents in the same di

Question

Two long, parallel conductors separated by 10.0 cm carry currents in the same direction. The first wire carries current I1 = 6.00 A, and the second carries I2 = 8.00 A. (Assume the conductors lie in the plane of the page.)

(a) What is the magnitude of the magnetic field created by I1 and acting on I2? ______T _______ Direction

(b) What is the force per unit length exerted on I2 by I1? ______N/m _______ Direction

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

(d) What is the force per length exerted by I2 on I1? ______N/m _______ Direction

Explanation / Answer

Given data

Distance between the conductors, r = 0.10 m

Current carried by the first wire, I1 = 6.00 A

Current carried by the second wire, I2 = 8.00 A

(a) the magnitude of the magnetic field created by I1 and acting on I2 is

B1 = (uo/2*pi)*(I1/r)

= 2*10^-7 * (6.00/0.10)

= 12*10^-6 T

Magnitude of B1 = 12 micro T

Direction is +ve z-direction

(b)
F2 = B1 * I2 * L

= 12*10^-6 * 8 * 1

= 9.6*10^-5 N

Magnitude of B1 = 9.6*10^-5 N

Direction is -ve y direction

(c)
B2 = (uo/2*pi)*(I2/r)

= 2*10^-7 * (8.00/0.10)
  
= 16*10^-6 T

Magnitude of B2 = 16 micro T

Direction is -ve z-direction

(d)
F1 = B2 * I1 * L
  
= 16*10^-6 * 6 * 1

= 9.6*10^-5 N

Magnitude of B1 = 9.6*10^-5 N

Direction is +ve y direction

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