Step 1: Understanding the Concept:
Every current-carrying conductor generates a magnetic field around it according to Ampere's Law.
When a second conductor is placed within this field, the moving charges in that conductor experience a magnetic force (Lorentz Force).
This leads to a mutual force interaction between the two parallel wires.
Step 2: Key Formula or Approach:
The direction of the force can be determined by combining the Right-Hand Grip Rule (for the field) and the Right-Hand Palm Rule (for the force).
The magnitude of force per unit length is given by:
\[ \frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi r} \]
Step 3: Detailed Explanation:
Let's analyze the interaction step-by-step:
1. Assume wire 1 is carrying current \(I_1\) vertically upward.
2. Using the right-hand grip rule (thumb in direction of current), your fingers wrap around the wire. At the position of wire 2 (to its right), the magnetic field \(\vec{B}_1\) points "into the page".
3. Now, consider wire 2 carrying current \(I_2\) vertically upward within this field \(\vec{B}_1\).
4. Apply the right-hand force rule: Point your thumb upward (current \(I_2\)) and fingers into the page (field \(\vec{B}_1\)). Your palm points left, toward wire 1.
5. By Newton's Third Law, wire 1 experiences an equal and opposite force pointing toward wire 2.
Because both wires are being pulled toward one another, the interaction is attractive.
Step 4: Final Answer:
Parallel currents in the same direction always result in an attractive force.