Question

Two long, straight parallel wires separated by a distance \( r \) carry steady currents \( I_1 \) and \( I_2 \) in the exact same direction. What type of magnetic force interaction do they experience?

• A. \( \text{A repulsive force driving them apart.} \)
• B. \( \text{Zero force interaction because the lines run parallel.} \)
• C. \( \text{An attractive force pulling them together.} \)
• D. \( \text{A rotational torque twisting them perpendicular to each other.} \)

Hint:

Remember this handy rule: Parallel currents attract, antiparallel currents repel. This is the exact opposite behavior of electric charges, where like charges repel and opposite charges attract.

Answer 1

The Correct Option is C

Concept: A current-carrying wire sets up a magnetic field around itself according to Ampere's Law. When a second current-carrying wire is placed inside this magnetic field, its moving charges experience a Lorentz force, leading to a mutual force interaction between the wires.

Step 1: Determine the field direction using the right-hand grip rule. Let wire 1 carry current \( I_1 \) vertically upward. According to the right-hand thumb rule, wrapping your fingers around the wire shows that its magnetic field \( \vec{B}_1 \) points into the page at the position of wire 2.

Step 2: Apply the Lorentz force cross-product rule to find the force direction. Wire 2 carries a current \( I_2 \) vertically upward within this magnetic field pointing into the page. Using the magnetic force law for a current element \( \vec{F} = I(\vec{L} \times \vec{B}) \), we point our fingers upward along the current path and curl them into the page toward the field lines. Your thumb points leftward, directly toward wire 1. By Newton's third law, wire 1 experiences an equal and opposite force pointing rightward toward wire 2. This mutual attraction pulls the two parallel lines together.