Question

Magnetic Force Between Two Paralle
Current Carrying Conducting Wires​

Answer 1

Explanation:

The official definition of the ampere is: One ampere of current through each of two parallel conductors of infinite length, separated by one meter in empty space free of other magnetic fields, causes a force of exactly 2 × 10−7 N/m on each conductor.

Answer 2

Explanation:

Consider two infinite parallel straight wires, a distance h apart, carrying upwards currents, I1 and I2 , respectively, as illustrated in Figure 22.2.1 .

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Figure 22.2.1 : Two parallel current-carrying wires will exert an attractive force on each other, if their currents are in the same direction.

The first wire will create a magnetic field, B⃗ 1 , in the shape of circles concentric with the wire. At the position of the second wire, the magnetic field B1 is into the page, and has a magnitude:

B1=μ0I12πh

Since the second wire carries a current, I2 , upwards, it will experience a magnetic force, F⃗ 2 , from the magnetic field, B1 , that is towards the left (as illustrated in Figure 22.2.1 and determined from the right-hand rule). The magnetic force, F⃗ 2 , exerted on a section of length, l , on the second wire has a magnitude given by:

F2=I2||l⃗ ×B⃗ 1||=I2lB1μ0I2I1l2πh

where we used the fact that the angle between l⃗ and B⃗ is 90◦ . We expect, from Newton’s Third Law, that an equal and opposite force should be exerted on the first wire. Indeed, the second wire will create a magnetic field, B⃗ 2 , that is out of the page at the location of the first wire, with magnitude:

B2=μ0I22πh

This leads to a magnetic force, F⃗ 1 , exerted on the first wire, that points to the right (from the right-hand rule).

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