Question

Two parallel wires are separated by 0.25 m. Wire A carries 5.0 A and Wire B carries 10 A, both currents in the same direction. What is the force on 0.80 m of Wire A?

Answer 1

Using Ampere's Law and the formula for calculating the magnetic field produced by one wire at the location of another, we can find the force on a wire. In this case, the force on 0.80 m of Wire A is calculated to be 6.4 × 10⁻⁶ N.

Step-by-step explanation:

The force on a wire can be calculated using Ampere's Law. In this case, we can find the force on wire A by considering the magnetic field produced by wire B at the location of wire A.

Since the wires are parallel, the magnetic field produced by wire B at the location of wire A can be calculated using the formula:

B = (μ₀ × I) / (2π × r)

Where μ₀ is the permeability of free space, I is the current in wire B, and r is the distance between the wires.

Substituting the values given in the question (μ₀ = 4π × 10⁻⁷ T·m/A, I = 10 A, r = 0.25 m) into the formula, we can find the magnetic field produced by wire B at the location of wire A:

B = (4π × 10⁻⁷ T·m/A × 10 A) / (2π × 0.25 m)

Simplifying the expression, we find that the magnetic field produced by wire B at the location of wire A is 1.6 × 10⁻⁶ T.

The force on wire A can then be calculated using the equation:

F = I × B × L

Where F is the force, I is the current in wire A, B is the magnetic field, and L is the length of wire A.

Substituting the values given in the question (I = 5 A, B = 1.6 × 10⁻⁶ T, L = 0.8 m) into the equation, we can find the force on wire A:

F = 5 A × 1.6 × 10⁻⁶ T × 0.8 m

Simplifying the expression, we find that the force on 0.80 m of wire A is 6.4 × 10⁻⁶ N.

Answer 2

The student's question is about the magnetic force on a section of wire due to another current-carrying wire. To solve for the force, we use the formula considering the magnitude of currents, length of wire, and separation distance to find the attractive force.

Step-by-step explanation:

The question involves calculating the magnetic force exerted on a section of wire due to the magnetic field created by a current in a parallel wire. Using the formula for the force between two parallel currents, which is F = (μ_0 × I_1 × I_2 × L) / (2π × d), where F is the force, μ_0 is the magnetic constant (4π × 10−7 T·m/A), I_1 and I_2 are the currents in the wires, L is the length of the wire, and d is the distance between the wires. Given that Wire A carries 5 A and Wire B carries 10 A, and they are separated by 0.25 m, the force on 0.80 m of Wire A can be found by plugging these values into the formula. The fact that both currents are in the same direction means they will exert an attractive force on each other.