mutual force interaction of two parallel conductors with current

1. Explain the mutual force interaction between two parallel current-carrying conductors.

Solution:

Two straight, parallel conductors through which electric currents flow exert magnetic forces on each other. If currents flow in the same direction, they attract; if they flow in opposite directions, they repel.

Fm=μ0μr2π⋅I1I2ldF_m = \frac{\mu_0 \mu_r}{2\pi} \cdot \frac{I_1 I_2 l}{d}

For air:

Fm=k⋅I1I2ld,wherek=μ0μr2π=2×10−7 N⋅A−2F_m = k \cdot \frac{I_1 I_2 l}{d}, \quad \text{where} \quad k = \frac{\mu_0 \mu_r}{2\pi} = 2 \times 10^{-7} \, N \cdot A^{-2}

 

I1, I2 = electric currents, d = distance between conductors, l = active length of the conductor,

2.Two long, straight, parallel conductors in air separated by 1 m carry equal currents I1 = I2 = 1 A. Calculate the magnitude of the force that acts per unit length of each conductor.

Solution:

Given:

I1 = I2 = 1 A,   l = 1 m,  d = 1 m,  k = 2.10-7 N·A-2

vzajomne-silove-posobenie-rovnobeznych-prudov-2.gif 

The required force is Fm = 2.10–7 N.

This example follows from the definition of the ampere—the base unit of electric current in SI.

The ampere is the constant current which, if maintained in two straight, parallel, infinitely long conductors of negligible cross-section, placed in vacuum and at a distance of 1 m from each other, would produce a force of 2.10–7 N per 1 m of length between these conductors.

3.Between two parallel conductors of a high-current line, separated by 20 cm, a force of 16 N acts on each meter of conductor length. Determine the magnitude of the electric current in the line.

Solution:

Given:

vzajomne-silove-posobenie-rovnobeznych-prudov-3.gif 

The line current is I1 = I2 = I = 4000 A.

4.At what distance must two parallel straight conductors be separated if each carries a current of 50 A and they exert a mutual force of 0.01 N per 1 m of length?

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5.An electric current flows through two straight, parallel conductors connected in series. By what factor must this current be increased so that, when the distance between the conductors is doubled, the magnitudes of the forces acting on the conductors remain unchanged?

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6.Two parallel conductors 10 cm apart carry identical currents of 1000 A. Determine the active length of the conductors if a force of 2 N acts on them.

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7.Two parallel conductors 10 cm apart carry identical currents. Determine the magnitude of the current flowing through the conductors if a force of 1.8 N acts on 1 meter of their length.

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8.Two straight parallel conductors with a length of 50 m and currents of 300 A at a distance of 5 cm experience a magnetic force of 5400 N. A piece of nickel is placed between the conductors. Determine the relative permeability of the nickel.

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9.Two very long straight conductors at a mutual distance d = 10 cm carry currents I1 = 10 A,

I2 = 15 A in the same direction. Determine the magnitude of the magnetic field intensity H at point Q located halfway between the conductors.

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10.Express the units of magnetic flux density B, magnetic field intensity H, and magnetic force Fm as a product of the SI base units.

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