Two long, parallel wires carry current in the x-y plane. One wire carries 30 A to the left along the x-axis. The other carries 50 A to the right along a parallel line at y = 0.28 m. At what y-axis position in meters is the magnetic field equal to zero?
20. A projectile is fired with an initial velocity of 88 ft/sec at an angle of 35° to the
horizontal. Neglecting air resistance, what is the time of impact? (Round to the
nearest tenth of a second.)
Remember: x = (v0 cos θ)t and y = h0 + (v0sinθ)t – 16 t^2
μ₀I₁/2πy= μ₀I₂/2π(0.28-y)
I₁(0.28-y)= I₂y
30(0.28-y)=50y
80y=8.4
y=8.4/80=0.105 m
To determine at what y-axis position the magnetic field is equal to zero, we can use the Biot-Savart law.
The Biot-Savart law states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire. It can be given by the equation:
B = (μ₀⁄4π) * (I * dl * sinθ) ⁄ r²
where B is the magnetic field, μ₀ is the permeability of free space (4π × 10⁻⁷ T⋅m/A), I is the current, dl is a small segment of the wire carrying the current, θ is the angle between dl and the displacement vector from the wire to the point, and r is the distance from the wire to the point.
In this scenario, we have two wires. Let's consider the magnetic field at a point on the y-axis, at a distance y from the x-axis wire (which carries 30 A).
For the first wire carrying 30 A, the magnetic field at the y-axis point is given by:
B₁ = (μ₀⁄4π) * (30 A * dl₁ * sinθ₁) ⁄ r₁²
For the second wire, with a current of 50 A, the magnetic field at the y-axis point is given by:
B₂ = (μ₀⁄4π) * (50 A * dl₂ * sinθ₂) ⁄ r₂²
Since dl₁ and dl₂ are parallel to the y-axis and perpendicular to the displacement vector from the wire to the point, their sinθ values are equal to 1.
Now, we need to note that the total magnetic field at the y-axis point is the vector sum of the magnetic fields produced by the two wires:
B_total = B₁ + B₂
To find the y-axis position where the magnetic field is zero, we need to set B_total equal to zero:
B_total = B₁ + B₂ = 0
Now, we have an equation that relates the magnetic field at the y-axis point to the distances and currents in the wires. However, the lengths of dl₁ and dl₂ are missing from the problem description, so we cannot solve for the exact y-axis position where the magnetic field is zero without that information.
To continue, we would need additional information about the lengths or positions of the wires.