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1. Find the magnetic field at the midpoint between two infinitely long parallel wires with steady current I, and find the force per unit length between them. The distance between the two wires is d. Draw the forces and magnetic field everywhere in space. 2. Find the magnetic field at the midpoint between two infinitely long anti-parallel wires with steady current I, and find the force per unit length between them. The distance between the two wires is d. Draw the forces and magnetic field everywhere in space.

1. Find the magnetic field at the midpoint between two infinitely long parallel wires with steady current I, and find the force per unit length between them. The distance between the two wires is d. Draw the forces and magnetic field everywhere in space. 2. Find the magnetic field at the midpoint between two infinitely long anti-parallel wires with steady current I, and find the force per unit length between them. The distance between the two wires is d. Draw the forces and magnetic field everywhere in space.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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### Magnetism in Parallel and Anti-Parallel Current-Carrying Wires #### 1. Magnetic Field Between Two Infinitely Long Parallel Wires **Problem Statement:** Find the magnetic field at the midpoint between two infinitely long parallel wires with a steady current \( I \), and find the force per unit length between them. The distance between the two wires is \( d \). Draw the forces and magnetic field everywhere in space. **Solution:** - **Magnetic Field Calculation:** The magnetic field generated by a long straight wire with current \( I \) at a distance \( r \) from the wire is given by Ampere’s Law: \[ B = \frac{\mu_0 I}{2 \pi r} \] where \( \mu_0 \) is the permeability of free space. At the midpoint between the two wires, the distance from each wire is \( \frac{d}{2} \). The magnetic fields due to each wire will add up vectorially. Since the wires carry current in the same direction, the magnetic fields at the midpoint will have the same magnitude but opposite directions. The total magnetic field at the midpoint is therefore: \[ B_{total} = 2 \times \frac{\mu_0 I}{2 \pi \left( \frac{d}{2} \right)} = \frac{\mu_0 I}{\pi \left( \frac{d}{2} \right)} = \frac{2 \mu_0 I}{\pi d} \] - **Force Per Unit Length Calculation:** The force per unit length between two parallel wires carrying current in the same direction is given by: \[ F = \frac{\mu_0 I^2}{2 \pi d} \] - **Diagram:** Draw two parallel wires a distance \( d \) apart. Indicate the direction of the current in both wires and the resulting magnetic field lines with arrows. The magnetic field at the midpoint is directed perpendicularly to the plane containing the wires. #### 2. Magnetic Field Between Two Infinitely Long Anti-Parallel Wires **Problem Statement:** Find the magnetic field at the midpoint between two infinitely long anti-parallel wires with a steady current \( I \), and find the force per unit length between them. The distance between the two wires is \( d \). Draw
Transcribed Image Text:### Magnetism in Parallel and Anti-Parallel Current-Carrying Wires #### 1. Magnetic Field Between Two Infinitely Long Parallel Wires **Problem Statement:** Find the magnetic field at the midpoint between two infinitely long parallel wires with a steady current \( I \), and find the force per unit length between them. The distance between the two wires is \( d \). Draw the forces and magnetic field everywhere in space. **Solution:** - **Magnetic Field Calculation:** The magnetic field generated by a long straight wire with current \( I \) at a distance \( r \) from the wire is given by Ampere’s Law: \[ B = \frac{\mu_0 I}{2 \pi r} \] where \( \mu_0 \) is the permeability of free space. At the midpoint between the two wires, the distance from each wire is \( \frac{d}{2} \). The magnetic fields due to each wire will add up vectorially. Since the wires carry current in the same direction, the magnetic fields at the midpoint will have the same magnitude but opposite directions. The total magnetic field at the midpoint is therefore: \[ B_{total} = 2 \times \frac{\mu_0 I}{2 \pi \left( \frac{d}{2} \right)} = \frac{\mu_0 I}{\pi \left( \frac{d}{2} \right)} = \frac{2 \mu_0 I}{\pi d} \] - **Force Per Unit Length Calculation:** The force per unit length between two parallel wires carrying current in the same direction is given by: \[ F = \frac{\mu_0 I^2}{2 \pi d} \] - **Diagram:** Draw two parallel wires a distance \( d \) apart. Indicate the direction of the current in both wires and the resulting magnetic field lines with arrows. The magnetic field at the midpoint is directed perpendicularly to the plane containing the wires. #### 2. Magnetic Field Between Two Infinitely Long Anti-Parallel Wires **Problem Statement:** Find the magnetic field at the midpoint between two infinitely long anti-parallel wires with a steady current \( I \), and find the force per unit length between them. The distance between the two wires is \( d \). Draw
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