I know how to do this problem, but I am having a difficult time figuring out the distance . I thought that from wire 1 to P2 the distance is 45 cm, and the distance from wire 2 to the p2 the distance is 35 cm. However, I believe I am wrong, can someone please explain o me where my mistake it .

Question

I know how to do this problem, but I am having a difficult time figuring out the distance . I thought that from wire 1 to P2 the distance is 45 cm, and the distance from wire 2 to the p2 the distance is 35 cm. However, I believe I am wrong, can someone please explain o me where my mistake it .

Question: Two long, straight parallel wires are 10.0 cm apart and carry 3.80 A currents in the same direction. Find the magnitude of the magnetic field at point P2 , 35.0cm to the right of P1.

Answer 1

I am not certain of the orientation of the wires and P2, are they all in the same plane? Where is P1?

Answer 2

they are in the same plane

I1-----P1------I2---------P2
The current are both out of the plane.

Answer 3

To find the magnetic field at point P2, we can use Ampere's law. Ampere's law states that the magnetic field (B) around a closed loop is directly proportional to the current passing through the loop (I) and inversely proportional to the distance from the wire (r).

First, let's determine the distance from each wire to point P2. We're given that the two wires are 10.0 cm apart, so the distance from wire 1 to P2 will be half of that, which is 5.0 cm (or 0.05 m). Similarly, the distance from wire 2 to P2 will also be 5.0 cm.

Now that we have the correct distances, we can use Ampere's law to find the magnetic field at point P2 for each wire. Ampere's law formula for a straight wire is expressed as:

B = (μ₀ * I) / (2π * r)

Where:
B = Magnetic field in Teslas
μ₀ = Permeability of free space (constant value of 4π * 10^-7 Tm/A)
I = Current in Amperes
r = Distance from wire in meters

For wire 1:
B₁ = (4π * 10^-7 Tm/A * 3.80 A) / (2π * 0.05 m)

Simplifying:
B₁ = (2 * 10^-7 Tm/A * 3.80 A) / (0.05 m)

Calculating:
B₁ = (7.6 * 10^-7 Tm) / (0.05 m)
B₁ = 1.52 * 10^-5 T

So, the magnitude of the magnetic field produced by wire 1 at point P2 is 1.52 * 10^-5 Tesla.

Repeating the process for wire 2:
B₂ = (4π * 10^-7 Tm/A * 3.80 A) / (2π * 0.05 m)

Simplifying:
B₂ = (2 * 10^-7 Tm/A * 3.80 A) / (0.05 m)

Calculating:
B₂ = (7.6 * 10^-7 Tm) / (0.05 m)
B₂ = 1.52 * 10^-5 T

So, the magnitude of the magnetic field produced by wire 2 at point P2 is also 1.52 * 10^-5 Tesla.

To find the total magnetic field at point P2 due to the two wires carrying current in the same direction, we can simply add the magnitudes of the magnetic fields:

B_total = B₁ + B₂
B_total = 1.52 * 10^-5 T + 1.52 * 10^-5 T
B_total = 3.04 * 10^-5 T

Therefore, the magnitude of the magnetic field at point P2, located 35.0 cm to the right of P1, is 3.04 * 10^-5 Tesla.