Two long straight wires pierce the plane of the paper at vertices of an equilateral triangle as shown below. They each carry 2 A, out of the paper. The magnetic field at the third vertex (P) has magnitude (in T):

Question

Quizplus · Accepted Answer

The magnetic field at point P can be found using the Biot-Savart law, which states that the magnitude of the magnetic field due to a current-carrying wire at a point is proportional to the current and the distance from the point to the wire. Since the two wires are carrying equal current and are equidistant from point P, their magnetic fields at point P will add together. Using the equation for the magnetic field due to a straight wire, we can calculate the magnetic field due to each wire as:
B = μ0I/2πr
where μ0 is the permeability of free space (equal to 4π×10^-7 T m/A), I is the current, and r is the distance from the wire to the point.
For each wire, the distance from the wire to point P is one side length of the equilateral triangle, which we can call a. Therefore, the magnetic field due to each wire is:
B1 = μ0(2 A)/2πa
Using the triangle formed by the wires and point P, we can see that the angle between the wires is 60 degrees, so the distance from each wire to point P is equal to a*cos(60) = a/2. The magnetic field due to each wire can thus be expressed as:
B1 = μ0(4 A)/2πa
The magnetic field at point P due to both wires is the sum of the individual magnetic fields, so we have:
BP = B1 + B2 = μ0(8 A)/2πa
Substituting in the given value of a (equal to 0.1 m), we get:
BP = (4π×10^-7 T m/A)(8 A)/(2π)(0.1 m) = 1.6×10^-5 T
Rounding to one significant figure, we get:
BP ≈ 2×10^-5 T
which is closest to the value given in choice B. Therefore, the best choice is B.

Two Long Straight Wires Pierce the Plane of the Paper