. A current of 21A is passed
through a 20m length of two
conducting wire placed 125cm
apart. Determine the force of
attraction between the wires
assuming the current is flowing in
the direction.
A. 1.33 x 10-5N
B. 4.5 x 10-5N
C. 7.1 x 10-5N
D. 6.4 x 10-5N
To determine the force of attraction between the wires, we can use the formula:
Force = (μ₀ * I₁ * I₂ * L) / (2 * π * d)
Where:
- Force is the force of attraction between the wires,
- μ₀ is the permeability of free space, equal to 4π x 10^(-7) N/A²,
- I₁ is the current passing through the first wire,
- I₂ is the current passing through the second wire,
- L is the length of the wire,
- d is the distance between the wires.
In this case, the current passing through both wires is the same, so we can substitute I₁ = I₂ = 21A. The length of the wire is given as 20m, and the distance between the wires is given as 125cm = 1.25m.
Plugging these values into the formula:
Force = (4π x 10^(-7) N/A² * 21A * 21A * 20m) / (2 * π * 1.25m)
= (4 * 21² * 10^(-7) N * m / A²) / (2 * 1.25)
Simplifying the expression:
Force = (4 * 441 * 10^(-7)) / 2.5
= 1764 * 10^(-7) / 2.5
= 7056 * 10^(-8) / 25
= 282.24 * 10^(-8) N
= 2.8224 * 10^(-5) N
Rounding the result to two decimal places, we get:
Force ≈ 2.82 x 10^(-5) N
The correct answer is not listed in the given options.
To determine the force of attraction between the wires, we can use Ampere's law. Ampere's law states that the magnetic field produced by a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.
The formula for the magnetic field produced by a current-carrying wire is:
B = (μ₀ * I) / (2π * r)
where B is the magnetic field, μ₀ is the permeability of free space (4π x 10^-7 Tm/A), I is the current, and r is the distance from the wire.
In this case, the current is 21A and the distance between the wires is 125 cm or 1.25 m.
Plugging in the values:
B = (4π x 10^-7 Tm/A * 21A) / (2π * 1.25m)
B = (3.36 x 10^-6 Tm) / (2.50m)
B = 1.344 x 10^-6 T
Now, the force of attraction between the wires can be calculated using the formula:
F = B * I * L
where F is the force of attraction, B is the magnetic field, I is the current, and L is the length of the wire.
Plugging in the values:
F = (1.344 x 10^-6 T) * 21A * 20m
F = 5.65 x 10^-4 N
Therefore, the force of attraction between the wires is approximately 5.65 x 10^-4 N.
The correct answer is not available among the options provided.