Two wires separated by a distance of 22 cm carry currents in the same direction.

Question

Two wires separated by a distance of 22 cm carry currents in the same direction. The current in one wire is I1 = 1.5 A, and the current in the other wire is I2 = 4.5 A.(Figure 1)
The current I1 is adjusted until the magnetic field halfway between the wires has a magnitude of 2.5×106 T and points into the page. Everything else in the system remains the same.

Find the magnitude of I1.

Express your answer using two significant figures. (in A)

Find the direction of I1. (to the left or to the right?)

Explanation / Answer

Let
I(1) be the current in one wire (A)
I(2) be the current in the other wire (A)
r = distance between the wires (m)
o= permeability of free space (N m^-2)

Then, from Ampere's law we have

B 1= o I(1) / 2r

B2 = o I(1) / 2r

solution

= o I(1) / 2r - o I(1) /2 r
where r=22/2=11cm

putting the value and you will get the answer

two wires carrying current in the same direction attract each othe

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