An infinitely long wire carrying a current of 2 A is bent at a right angle as shown in the Figure. What is the magnetic field magnitude in Tesla a point P, 10 cm from the corner?
I can not draw pic here but I will try to describe it:
Point P is in right side straight from bend place. and y-axis (I mean from where it is bending ) is pointing down. X_axis is straight(as we know), and Y_axis is pointing down. Current I_1 in X_axis is flowing in opposite direction from point P, but I_2 in Y-axis is flowing upwards.
http://www.jiskha.com/display.cgi?id=1385735645
To find the magnetic field magnitude at point P, we can use the Biot-Savart law, which states that the magnetic field created by a current-carrying wire at a point is directly proportional to the current and inversely proportional to the distance from the wire.
To calculate the magnetic field at point P, we need to sum the contributions from both segments of the wire.
Let's assume that the distance between the bend and point P is D, and the separation between the two wires is L.
First, let's calculate the magnetic field created by the wire segment carrying current I₁ along the x-axis at point P.
The magnetic field dB₁ created by a small segment of length dl carrying current I₁ is given by:
dB₁ = (μ₀ / 4π) * (I₁ * dl × r₁ / r₁³)
where:
- μ₀ is the permeability of free space, which is a constant equal to 4π × 10⁻⁷ T·m/A.
- I₁ is the current in the wire segment along the x-axis.
- dl is the length element of the wire.
- r₁ is the distance between the wire segment and point P.
Since the wire segment is aligned with the x-axis, the magnitude of vector dl × r₁ simplifies to dl * r₁.
Therefore, dB₁ = (μ₀ / 4π) * (I₁ * dl * r₁ / r₁³) = (μ₀ * I₁ * dl) / (4π * r₁²)
Integrating this expression over the entire length of the wire segment along the x-axis will give us the total magnetic field created by that wire segment at point P.
Next, let's calculate the magnetic field created by the wire segment carrying current I₂ along the y-axis at point P.
Similarly, the magnetic field dB₂ created by a small segment of length dl carrying current I₂ is given by:
dB₂ = (μ₀ / 4π) * (I₂ * dl × r₂ / r₂³)
where:
- I₂ is the current in the wire segment along the y-axis.
- r₂ is the distance between the wire segment and point P.
Since the wire segment is aligned with the y-axis, the magnitude of vector dl × r₂ simplifies to dl * r₂.
Therefore, dB₂ = (μ₀ / 4π) * (I₂ * dl * r₂ / r₂³) = (μ₀ * I₂ * dl) / (4π * r₂²)
Integrating this expression over the entire length of the wire segment along the y-axis will give us the total magnetic field created by that wire segment at point P.
Finally, to find the total magnetic field at point P, we can add the magnetic fields created by the two wire segments, dB₁ and dB₂, vectorially.
B_total = √(dB₁² + dB₂²)
You can substitute the values of I₁, I₂, dl, r₁, and r₂ into the equations and evaluate the integrals to find the magnetic field magnitude at point P.