A current of 21A is passed through a 20m length of two conducting wire placed 125 cm apart.Determine the force of attraction between the wires assuming the current is flowing in the direction
Oh, I see we're discussing some shocking business here! Well, let me electrify you with the answer!
The force of attraction between the wires can be determined using Ampere's law, which states that the force between two parallel conductors is proportional to the product of the currents and inversely proportional to the distance between them.
F = (μ₀ * I₁ * I₂ * L) / (2 * π * d)
Where:
F is the force of attraction between the wires
μ₀ is the permeability of free space (4π × 10^⁻7 T m/A)
I₁ and I₂ are the currents in the wires, both equal to 21A
L is the length of the wire, which is 20m
d is the distance between the wires, which is 125cm or 1.25m
Plugging in the values, we get:
F = (4π × 10^⁻7 T m/A * 21A * 21A * 20m) / (2 * π * 1.25m)
Simplifying:
F = (4 * 3.14 × 10^⁻7 * 441 * 20) / 2.5
F = (8.826 × 10^⁻5) / 2.5
F ≈ 3.53 × 10^⁻5 N
So, the force of attraction between the wires is approximately 3.53 × 10^⁻5 Newtons. That's quite the electric attraction, wouldn't you say?
To determine the force of attraction between the wires, we can use Ampere's Law. Ampere's Law states that the magnetic field (B) produced by a current-carrying wire is directly proportional to the current (I) and inversely proportional to the distance (r) between the wires.
The formula to calculate the magnetic field between two parallel wires 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 between the wires.
Let's calculate the magnetic field first:
B = (4π x 10^-7 Tm/A * 21A) / (2π * 0.125m)
B = (4 * 21) / (0.125)
B = 84 / 0.125
B = 672 T
Now, the force of attraction between the wires can be calculated using the formula:
F = (μ₀ * I^2 * l) / (2π * r)
Where F is the force of attraction, μ₀ is the permeability of free space, I is the current, l is the length of the wire, and r is the distance between the wires.
Plugging in the values:
F = (4π x 10^-7 Tm/A * (21A)^2 * 20m) / (2π * 0.125m)
F = (4π x 10^-7 Tm/A * 441A^2 * 20m) / (2π * 0.125m)
F = (1764 * 20) / (0.125)
F = 35280 / 0.125
F = 282240 N
Therefore, the force of attraction between the wires is 282,240 Newtons.
To determine the force of attraction between the wires, we can use Ampere's Law, which states that the magnetic field produced by a current-carrying wire is directly proportional to the current and inversely proportional to the distance between the wires.
The formula for the magnetic field between two parallel wires is given by:
B = (μ0 * I) / (2 * π * d)
Where:
B is the magnetic field strength
μ0 is the permeability of free space (4π × 10^-7 T·m/A)
I is the current passing through the wires
d is the distance between the wires
First, we need to convert the distance between the wires into meters:
125 cm = 1.25 m
Now, we can plug in the given values into the formula to calculate the magnetic field strength:
B = (4π × 10^-7 T·m/A * 21 A) / (2 * π * 0.0125 m)
Simplifying the formula:
B = (2 × 10^-7 T·m/A * 21 A) / (0.025 m)
Calculating the numerator:
2 × 10^-7 T·m/A * 21 A = 4.2 × 10^-6 T·m
Substituting the values back into the formula:
B = (4.2 × 10^-6 T·m) / (0.025 m)
Simplifying the formula:
B = 0.168 T
Now that we have the magnetic field strength, we can calculate the force of attraction between the wires by using the formula:
F = B * I * d
Substituting the values into the formula:
F = (0.168 T) * (21 A) * (0.0125 m)
Calculating the force of attraction:
F = 0.0441 N
Therefore, the force of attraction between the wires is 0.0441 Newtons.