### Magnetic Field and Current-Carrying Wire#### Problem StatementIn the figure to the right, a long straight current-carrying wire of linear mass density \( \mu \) is suspended by threads. A magnetic field perpendicular to the wire exerts a horizontal force that deflects the wire to an equilibrium angle \( \theta \). Find an expression for the strength and direction of the magnetic field \( \mathbf{B} \).#### Diagram ExplanationThe accompanying diagram illustrates a wire suspended by threads, with current \( I \) flowing through it. The wire is deflected at an angle \( \theta \) due to the force exerted by the magnetic field. The forces acting on the wire are depicted as follows:- A horizontal force \( \mathbf{F} \) exerted by the magnetic field.- The tension in the thread holding the wire.- The weight of the wire acting downwards.#### Solution OutlineTo find the magnetic field strength \( \mathbf{B} \), we will use the following known physical relationships and principles, involving magnetic force, tension, weight, and equilibrium of forces. The equilibrium condition will help us formulate the expression for \( \mathbf{B} \).

Linear mass density Angle Current

★5 In the figure to the right, a long straight current carrying wire of linear mass density μ is suspended by threads. A magnetic field perpendicular to the wire exerts a horizontal force that deflects the wire to an equilibrium angle 0. Find an expression for the strength and direction of the magnetic field B.

★5 In the figure to the right, a long straight current carrying wire of linear mass density μ is suspended by threads. A magnetic field perpendicular to the wire exerts a horizontal force that deflects the wire to an equilibrium angle 0. Find an expression for the strength and direction of the magnetic field B.

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 Field and Current-Carrying Wire

#### Problem Statement
In the figure to the right, a long straight current-carrying wire of linear mass density \( \mu \) is suspended by threads. A magnetic field perpendicular to the wire exerts a horizontal force that deflects the wire to an equilibrium angle \( \theta \). Find an expression for the strength and direction of the magnetic field \( \mathbf{B} \).

#### Diagram Explanation
The accompanying diagram illustrates a wire suspended by threads, with current \( I \) flowing through it. The wire is deflected at an angle \( \theta \) due to the force exerted by the magnetic field. The forces acting on the wire are depicted as follows:
- A horizontal force \( \mathbf{F} \) exerted by the magnetic field.
- The tension in the thread holding the wire.
- The weight of the wire acting downwards.

#### Solution Outline
To find the magnetic field strength \( \mathbf{B} \), we will use the following known physical relationships and principles, involving magnetic force, tension, weight, and equilibrium of forces. The equilibrium condition will help us formulate the expression for \( \mathbf{B} \).

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