Solved Examples: Calculating Force Per Unit Length Between Parallel Wires

📚 Quick Study Guide

• 𧲘 The force per unit length between two parallel wires is given by: $F/L = \frac{\mu_0 I_1 I_2}{2 \pi d}$, where $F$ is the force, $L$ is the length, $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} T \cdot m/A$), $I_1$ and $I_2$ are the currents in the wires, and $d$ is the distance between the wires.
• 🧭 If the currents are in the same direction, the force is attractive.
• ↔️ If the currents are in opposite directions, the force is repulsive.
• 📏 The force is proportional to the product of the currents and inversely proportional to the distance between the wires.

🧪 Practice Quiz

1. What is the force per unit length between two parallel wires carrying currents of 5A and 10A, separated by a distance of 0.1m?
   1. $1 \times 10^{-5} N/m$
   2. $2 \times 10^{-4} N/m$
   3. $1 \times 10^{-3} N/m$
   4. $4 \times 10^{-5} N/m$
2. Two parallel wires carry currents in opposite directions. What is the nature of the force between them?
   1. Attractive
   2. Repulsive
   3. Zero
   4. First attractive, then repulsive
3. If the distance between two parallel wires is doubled, what happens to the force per unit length?
   1. It doubles
   2. It halves
   3. It quadruples
   4. It remains the same
4. What is the value of the permeability of free space, $\mu_0$?
   1. $8.85 \times 10^{-12} F/m$
   2. $4\pi \times 10^{-7} T \cdot m/A$
   3. $3 \times 10^{8} m/s$
   4. $1.6 \times 10^{-19} C$
5. Two wires carry the same current in the same direction. At what point between the wires is the magnetic field zero?
   1. Midway between the wires
   2. Closer to the wire with higher current
   3. Closer to the wire with lower current
   4. The magnetic field is never zero
6. A wire carrying a current of 2A experiences a force per unit length of $4 \times 10^{-6} N/m$ due to another parallel wire 0.2m away. What is the current in the other wire?
   1. 1 A
   2. 2 A
   3. 4 A
   4. 0.5 A
7. If the currents in both wires are doubled, what happens to the force per unit length?
   1. It doubles
   2. It halves
   3. It quadruples
   4. It remains the same