Question

When seen from the end, three long, parallel wires form an Part A equilateral triangle 6.0 cm on a side. The wires each carry a 3.0 A current, with one current direction opposite the other two. What is the magnetic field strength at the center of the triangle? Express your answer with the appropriate units.

Answer 1

To calculate the magnetic field strength at the center of the triangle formed by the three wires, use the formula for the magnetic field due to a long straight wire. Substituting the given values, the magnetic field strength is found to be 2 × 10^-5 T.

Step-by-step explanation:

The magnetic field strength at the center of the triangle formed by the three long, parallel wires can be found using the formula for the magnetic field due to a long straight wire. The formula is given by:

B = (μ₀ * I) / (2π * r)

Where B is the magnetic field strength, μ₀ is the permeability of free space (4π × 10-7 T·m/A), I is the current in the wire, and r is the distance from the wire to the point where the magnetic field is being calculated.

In this case, the three wires each carry a current of 3.0 A and form an equilateral triangle with sides of 6.0 cm. The distance from the center of the triangle to each wire is half the side length, so r = 3.0 cm.

Substituting the given values into the formula:

B = (4π × 10-7 T·m/A * 3.0 A) / (2π * 0.03 m)

B = 2 × 10-5 T

Therefore, the magnetic field strength at the center of the triangle is 2 × 10-5 T.

Answer 2

The magnetic field strength at the center of an equilateral triangle formed by three parallel wires with equal currents, two in one direction and one in the opposite, is 0 T. This conclusion is reached because the magnetic fields produced by the wires cancel each other out.

Step-by-step explanation:

The question pertains to the calculation of the magnetic field strength at the center of an equilateral triangle formed by three long, parallel wires carrying currents. We are given that the triangle sides are 6.0 cm and each wire carries a 3.0 A current, with one current in the opposite direction of the other two. Using the right-hand rule, we know the magnetic field lines form concentric circles around the wire, and the strength of the magnetic field at a point due to a single long straight wire is given by B = (µ0 I) / (2π r), where B is the magnetic field strength, µ0 is the magnetic constant (4π x 10−12 T·m/A), I is the electric current, and r is the distance to the center of the triangle.

For an equilateral triangle, the distance from any vertex to the center is r = side / (√3), so r = 6.0 cm / (√3). Each wire contributes to the magnetic field at the center, but the net magnetic field is zero because the fields due to the two wires with current in the same direction cancel out with the field due to the wire with the opposite current direction. Therefore, the magnetic field strength at the center of the triangle is 0 T.