Question

The unit of current, the ampere, is defined in terms of the force between currents. Two 1.0-meter-long sections of very long wires a distance 1.5 m apart each carry a current of 1.0 A.

Required:
What is the force between them

Answer 1

The force between two parallel wires carrying current can be calculated using the formula F = (μ₀ × I₁ × I₂ × L) / (2πd), where F is the force, μ₀ is the permeability of free space, I₁ and I₂ are the currents in the wires, L is the length of the wires, and d is the distance between the wires. Plugging in the given values, the force between the wires is 2 × 10⁻⁷ N/m.

Step-by-step explanation:

The force between two parallel wires carrying current can be calculated using the formula:

F = \[\frac{{\mu_0 \cdot I_1 \cdot I_2 \cdot L}}{{2 \pi d}}\]

Where F is the force, \(\mu_0\) is the permeability of free space (\[4\pi \times 10^{-7} T \cdot m/A\]), \(I_1\) and \(I_2\) are the currents in the wires (in this case, 1 A), L is the length of the wires, and d is the distance between the wires (in this case, 1.5 m).

Plugging in the given values, the force between the wires is:

F = \[\frac{{4\pi \times 10^{-7} T \cdot m/A \cdot 1 A \cdot 1 A \cdot 1 m}}{{2 \pi \cdot 1.5 m}}\]

F = 2 \times 10^{-7} N/m

Answer 2

`1.33* 10^(-8) N`

Step-by-step explanation:

According to the given scenario, the computation of force between them is shown below:-

As we know that

`\mu = 4\pi* 10^(-7)`

The force between two current carrying wires will be

`F = (\mu_oI_1I_2L)/(2\pi r)`

`= (4\pi* 10^(-7) (1 A) (1 A) (1.0 m))/(2\pi (1.5m))`

`= 1.33* 10^(-7) N`

`= 1.33* 10^(-8) N`

Therefore for computing the force between two wires we simply applied the above formula.

So, the force between two wires carrying 1 A current
`= 1.33* 10^(-8) N`.