two straight parallel conductors carry current 200mA and 1A in opposite direction wires are 20 cm apart the distance of neutral point from 1A
To find the distance of the neutral point from the 1A conductor, we can use the concept of the magnetic field created by the two parallel conductors.
Step 1: Determine the magnetic field created by each conductor.
The magnetic field created by a long straight conductor can be found using Ampere's Law. The formula for the magnetic field at a point due to a current-carrying conductor is given by:
B = (μ₀ * I) / (2π * r)
Where:
B is the magnetic field strength
μ₀ is the permeability of free space (constant)
I is the current flowing through the conductor
r is the distance from the conductor
For the 1A conductor:
B₁ = (μ₀ * 1A) / (2π * r)
For the 200mA conductor:
B₂ = (μ₀ * 200mA) / (2π * r)
Step 2: Determine the net magnetic field at the neutral point.
Since the currents are flowing in opposite directions, the magnetic fields created by each conductor will have opposite directions as well. So the net magnetic field at the neutral point will be the difference between the magnitudes of the two magnetic fields:
B_net = |B₁ - B₂|
Step 3: Calculate the distance of the neutral point from the 1A conductor.
Given that the wires are 20 cm apart, the neutral point will be equidistant from each conductor. Let's call this distance x. So, the distance from the 1A conductor to the neutral point is x.
Now, let's substitute the values and solve for x.
B₁ = (μ₀ * 1A) / (2π * x)
B₂ = (μ₀ * 200mA) / (2π * (20cm - x))
B_net = |B₁ - B₂|
Now, we can solve for x using the equations above.
Please note that the permeability of free space (μ₀) is approximately 4π × 10⁻⁷ T·m/A.
To find the distance of the neutral point from the 1A conductor, we can use the concept of magnetic fields created by current-carrying conductors.
When two parallel conductors are carrying current in opposite directions, they create a magnetic field around themselves. At some point between the two conductors, the magnetic fields cancel out each other, resulting in a neutral point where the total magnetic field becomes zero.
To determine the distance of the neutral point from the 1A conductor, we can use the formula:
d = (I1 * L1) / (I1 + I2)
where:
d = distance of the neutral point from the 1A conductor,
I1 = current in the 200mA conductor,
I2 = current in the 1A conductor, and
L1 = distance between the two conductors.
Plugging in the values:
I1 = 0.2A,
I2 = 1A, and
L1 = 20cm = 0.2m (since it is given in cm),
d = (0.2 * 0.2) / (0.2 + 1)
= 0.04 / 1.2
= 0.0333 m (approximately)
Therefore, the distance of the neutral point from the 1A conductor is approximately 0.0333 meters or 33.3 cm.