Two long parallel wires carry unequal currents I1 and I2 in the same direction. Determine the values of currents I1 and I2. Two long parallel wires carry unequal currents I1 and I2 in the same direction. The ratio of the currents is 3 to 1. The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 µT. Determine the value of the currents I1 and I2.

Expert Answers

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The point where the magnetic field is measured lies at half distance between wires. Because of this, the magnetic fields that are generated by the same direction currents in the wires are opposite (one enters the paper and the other exits the paper).

By definition the magnetic induction at a distance R from a linear wire carrying the current I is

`B =(mu*I)/(2*pi*R)`

If we have two parallel wires, with currents I1 and I2 in the same direction we have (as discussed above)

`B_("tot") = B_1-B_2 =mu/(2*pi*R)*(I_1-I_2) =((3-1)*mu*I)/(2*pi*R) =(mu*I)/(pi*R)`

`I =(B_("tot")*pi*R)/mu = 4*10^-6*pi*0.1/(4*pi*10^-7)=1 A`

`I_1 =3*I =3 A` and `I_2 =I =1A`

The value of the currents in the wires are 3A and 1 A.

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