Magnetism and perpendicular wires.

[jenx44]

how do i find the b field of two perpendicular wires.

suppose one wire is pointing out of the page and the other one is going from left to right. I am looking for the magnetic field between them.

o (wire going out of paper)

B=?

xxxxxxxx (wire going left to right)

 

[antonantal]

You calculate the B vector produced by each wire alone in that point and then you sum the 2 vectors.

 

[kyle8921]

To find the magnetic field between two perpendicular wires, we can use the Biot-Savart Law. This law states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current in the wire and inversely proportional to the distance from the wire.

In this case, we have two wires perpendicular to each other, one pointing out of the page and the other going from left to right. We can break down the problem into two separate cases and then use the principle of superposition to find the total magnetic field.

Case 1: Wire going out of the page
Using the Biot-Savart Law, we can calculate the magnetic field at a point P between the two wires. The formula for the magnetic field at a point due to a wire is given by:

B = (μ0/4π) * (I/d)

Where μ0 is the permeability of free space, I is the current in the wire, and d is the distance from the wire to the point P.

In this case, the wire is pointing out of the page, so the current is flowing in the direction of our thumb if we use the right-hand rule. The distance from the wire to point P is the shortest distance, which is the distance between the two wires. We can call this distance d1.

Therefore, the magnetic field at point P due to the wire going out of the page is given by:

B1 = (μ0/4π) * (I1/d1)

Case 2: Wire going from left to right
Using the same formula, we can calculate the magnetic field at point P due to the wire going from left to right. In this case, the current is flowing in the direction of our fingers if we use the right-hand rule. The distance from the wire to point P is the shortest distance, which is again the distance between the two wires. We can call this distance d2.

Therefore, the magnetic field at point P due to the wire going from left to right is given by:

B2 = (μ0/4π) * (I2/d2)

Total magnetic field:
To find the total magnetic field at point P, we can use the principle of superposition, which states that the total magnetic field at a point due to multiple sources is the vector sum of the individual magnetic fields.

Therefore, the total magnetic field at point P is given by:

B = B