### Magnetic Fields and Forces Between Parallel Wires**Problem Statement:**1. Two straight parallel wires, running north/south, are separated by 10 cm and carry currents of 3A in the same direction (north). a) **Find the magnitude and direction of the magnetic field at a point midway between the wires.** b) **Find the magnetic field 6 cm east of the "easternmost" wire.** c) **Calculate the force of one wire on the other. Is it attractive or repulsive?****Explanation and Calculation:**When two parallel wires carry current in the same direction, they exert magnetic forces on each other. Here’s how to address these questions:### (a) Magnetic Field at MidpointUse Ampère’s law to find the magnetic field produced by each wire at a given point. The formula for the magnetic field due to a long, straight current-carrying wire is:\[ B = \frac{\mu_0 I}{2 \pi r} \]where:- \( B \) is the magnetic field,- \( \mu_0 \) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}\)),- \( I \) is the current,- \( r \) is the distance from the wire.### (b) Magnetic Field 6 cm East of Eastern WireCalculate the field at a point not equidistant from both wires to determine the superposition of the magnetic fields due to each wire:1. Calculate the magnetic field due to each wire at that point.2. Use vector addition to find the resultant magnetic field.### (c) Force Between the WiresThe force per unit length between two parallel currents is given by:\[ F/L = \frac{\mu_0 I_1 I_2}{2 \pi d} \]where \( d \) is the distance between the wires. The direction (attractive or repulsive) depends on whether currents are in the same or opposite directions.### ConclusionThrough these calculations, understand the interaction between magnetic fields and current-carrying wires, highlighting fundamental principles of electromagnetism and how currents can exert forces on one another. This has practical applications in electrical engineering and physics.

1. Two straight parallel wires, running north/south are separated by 10 cm and carry currents of 3A in the same direction (north). a) Find the magnitude and direction of the magnetic field at a point midway between the wires. b) Find the magnetic field 6 cm east of the "easternmost" wire. c) Calculate the force of one wire on the other. Is it attractive or repulsive?

1. Two straight parallel wires, running north/south are separated by 10 cm and carry currents of 3A in the same direction (north). a) Find the magnitude and direction of the magnetic field at a point midway between the wires. b) Find the magnetic field 6 cm east of the "easternmost" wire. c) Calculate the force of one wire on the other. Is it attractive or repulsive?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Magnetic Field Of Coaxial Cable

The word coaxial means same axis. So for a long straight cable to be coaxial, it must have concentric cylindrical shaped conductor around it. Coaxial cable (popularly called ‘coax’) has various applications ranging from current conductors to radiofrequency signal transmitters. This cable has lower emission losses and provides protection from electromagnetic interference which allows signals with less power to transmit over longer distances.For example, currents produced in the pickup of a stereo turntable generally travel to the amplifier through a coaxial cable.The self-inductance of a coaxial cable is another important characteristic, because it influences the propagation of electrical signals in the cable.

Question

### Magnetic Fields and Forces Between Parallel Wires

**Problem Statement:**

1. Two straight parallel wires, running north/south, are separated by 10 cm and carry currents of 3A in the same direction (north).

a) **Find the magnitude and direction of the magnetic field at a point midway between the wires.**

b) **Find the magnetic field 6 cm east of the "easternmost" wire.**

c) **Calculate the force of one wire on the other. Is it attractive or repulsive?**

**Explanation and Calculation:**

When two parallel wires carry current in the same direction, they exert magnetic forces on each other. Here’s how to address these questions:

### (a) Magnetic Field at Midpoint

Use Ampère’s law to find the magnetic field produced by each wire at a given point. The formula for the magnetic field due to a long, straight current-carrying wire is:

\[ B = \frac{\mu_0 I}{2 \pi r} \]

where:
- \( B \) is the magnetic field,
- \( \mu_0 \) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}\)),
- \( I \) is the current,
- \( r \) is the distance from the wire.

### (b) Magnetic Field 6 cm East of Eastern Wire

Calculate the field at a point not equidistant from both wires to determine the superposition of the magnetic fields due to each wire:

1. Calculate the magnetic field due to each wire at that point.
2. Use vector addition to find the resultant magnetic field.

### (c) Force Between the Wires

The force per unit length between two parallel currents is given by:

\[ F/L = \frac{\mu_0 I_1 I_2}{2 \pi d} \]

where \( d \) is the distance between the wires. The direction (attractive or repulsive) depends on whether currents are in the same or opposite directions.

### Conclusion

Through these calculations, understand the interaction between magnetic fields and current-carrying wires, highlighting fundamental principles of electromagnetism and how currents can exert forces on one another. This has practical applications in electrical engineering and physics.

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