Magnetic Force Physics Example 5

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Example 5

hard
Two parallel wires 0.1 m0.1 \text{ m} apart each carry 10 A10 \text{ A} in the same direction. What is the force per meter between them? Is it attractive or repulsive? Use μ0=4π×10−7 T m/A\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}.

Solution

  1. 1
    Force per unit length between parallel current-carrying wires: FL=μ0I1I22πd\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}.
  2. 2
    FL=4π×10−7×10×102π×0.1=4π×10−50.2π=2×10−4 N/m\frac{F}{L} = \frac{4\pi \times 10^{-7} \times 10 \times 10}{2\pi \times 0.1} = \frac{4\pi \times 10^{-5}}{0.2\pi} = 2 \times 10^{-4} \text{ N/m}
  3. 3
    Currents in the same direction attract each other.

Answer

FL=2×10−4 N/m (attractive)\frac{F}{L} = 2 \times 10^{-4} \text{ N/m (attractive)}
Parallel currents in the same direction create magnetic fields that attract the wires toward each other. Antiparallel currents repel. This force is the basis of the definition of the ampere.

About Magnetic Force

The force exerted on a moving charge or current-carrying conductor by a magnetic field.

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