* A and B Two wires long and parallel, each carrying a distance of 1 m in two opposite directions, if the trend A equals one third B (Ia=1/3Ib), founding after the point which lies on the line where the two vertical magnetic field when the outcome is zero.
This makes no sense to me.
I understand that the question may seem confusing at first. Let's break it down and try to understand it step by step.
We have two wires, A and B, that are parallel to each other. The distance each wire carries is given as 1 meter, but the directions are opposite for the two wires.
Now, the question mentions the current in wire A is one-third the current in wire B. It is represented as Ia = (1/3)Ib, where Ia is the current in wire A and Ib is the current in wire B.
The question asks for the point on the line between the two wires where the vertical magnetic field cancels out or becomes zero.
To solve this problem, we need to use Ampere's law, which relates the magnetic field around a closed loop to the electric current passing through the loop. We can use this law to find the magnetic field at different points between the two wires.
To apply Ampere's law, we consider a closed circular loop that goes around both wires A and B. The magnetic field created by wire A will be in the opposite direction to that of wire B. As we move along the loop, the magnetic fields add up or cancel out depending on the distance from the wires.
Now, according to Ampere's law, the magnetic field around a closed loop is proportional to the current passing through the loop. Therefore, the magnetic field on one side of the loop would be proportional to the current in wire A (Ia), and on the other side, it would be proportional to the current in wire B (Ib).
Since the currents in wire A and wire B are given by Ia = (1/3)Ib, the magnetic field contribution from wire A would be one-third of the magnetic field contribution from wire B at any point on the loop.
To find the point where the magnetic field becomes zero, we need to determine the location along the loop where the magnetic field contributions from both wires cancel each other out.
This can be done by assuming a distance (let's call it x) from wire B at which the magnetic field contributions from wires A and B cancel out. Since the magnetic field from wire A is one-third that of wire B, we can set up an equation:
(B due to wire A) = (B due to wire B)
By applying the formula for the magnetic field around a long straight wire (B = (μ0 * I) / (2 * π * r)), where μ0 is the permeability of free space, I is the current, and r is the distance from the wire, we can set up the equation as follows:
(μ0 * (1/3)Ib) / (2 * π * x) = (μ0 * Ib) / (2 * π * (1 - x))
Simplifying this equation will give us the value of x, which represents the distance from wire B where the vertical magnetic field is zero.
I hope this explanation helps in understanding the problem.