### Magnetic Forces on a Current-Carrying Rectangular Wire LoopA current-carrying rectangular wire loop with a width \( a = 0.115 \) m and length \( b = 0.215 \) m lies in the xy-plane, supported by a nonconducting, frictionless axle of negligible weight. A current of \( I = 2.25 \) A travels counterclockwise in the circuit (see the figure below). Calculate the magnitude and direction of the force exerted on the left, right, top, and bottom segments of the wire (in N) by a uniform magnetic field of \( 0.500 \) T that points in the positive x-direction. Find the magnitude of the net torque (in \( \text{N} \cdot \text{m} \)) on the loop about the axle.#### Diagram Explanation![Wire Loop Diagram](wire-loop-diagram.png)The diagram shows a rectangular loop of wire positioned horizontally in the xy-plane. It consists of left, right, top, and bottom segments. The loop is subjected to a magnetic field represented by the vector \( \mathbf{B} \), which points in the positive x-direction. The current flows counterclockwise, i.e., up through the left segment, right through the top segment, down through the right segment, and left through the bottom segment.Axes are labeled as follows:- \( x \)-axis: Horizontal direction to the right.- \( y \)-axis: Vertical direction upwards.- \( z \)-axis: Perpendicular to the xy-plane coming out of the page.### Task BreakdownUse the given variables to complete the following calculations:1. **Left Segment of the Wire**: - Magnitude of Force (N) - Direction of Force2. **Right Segment of the Wire**: - Magnitude of Force (N) - Direction of Force3. **Top Segment of the Wire**: - Magnitude of Force (N) - Direction of Force4. **Bottom Segment of the Wire**: - Magnitude of Force (N) - Direction of Force5. **Net Torque**: - Find the magnitude of the net torque on the loop about the axle.### HINT- Use the formula for the magnetic force on a current-carrying wire segment in a uniform magnetic field: \( \mathbf{F} = I

Given data:The width of loop is a=0.115 m.The length of loop is b=0.215 m.Magnitude of current is…

HINT (a) left segment of the wire magnitude direction ---Select-- (b) right segment of the wire magnitude direction (c) top segment magnitude direction --Select--- www ---Select--- (d) bottom segment magnitude direction ---Select-- N N N N (e) Find the magnitude of the net torque on the loop about the axle. N.m

HINT (a) left segment of the wire magnitude direction ---Select-- (b) right segment of the wire magnitude direction (c) top segment magnitude direction --Select--- www ---Select--- (d) bottom segment magnitude direction ---Select-- N N N N (e) Find the magnitude of the net torque on the loop about the axle. N.m

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.

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### Magnetic Forces on a Current-Carrying Rectangular Wire Loop

A current-carrying rectangular wire loop with a width \( a = 0.115 \) m and length \( b = 0.215 \) m lies in the xy-plane, supported by a nonconducting, frictionless axle of negligible weight. A current of \( I = 2.25 \) A travels counterclockwise in the circuit (see the figure below). Calculate the magnitude and direction of the force exerted on the left, right, top, and bottom segments of the wire (in N) by a uniform magnetic field of \( 0.500 \) T that points in the positive x-direction. Find the magnitude of the net torque (in \( \text{N} \cdot \text{m} \)) on the loop about the axle.

#### Diagram Explanation
![Wire Loop Diagram](wire-loop-diagram.png)

The diagram shows a rectangular loop of wire positioned horizontally in the xy-plane. It consists of left, right, top, and bottom segments. The loop is subjected to a magnetic field represented by the vector \( \mathbf{B} \), which points in the positive x-direction. The current flows counterclockwise, i.e., up through the left segment, right through the top segment, down through the right segment, and left through the bottom segment.

Axes are labeled as follows:
- \( x \)-axis: Horizontal direction to the right.
- \( y \)-axis: Vertical direction upwards.
- \( z \)-axis: Perpendicular to the xy-plane coming out of the page.

### Task Breakdown
Use the given variables to complete the following calculations:

1. **Left Segment of the Wire**:
- Magnitude of Force (N)
- Direction of Force

2. **Right Segment of the Wire**:
- Magnitude of Force (N)
- Direction of Force

3. **Top Segment of the Wire**:
- Magnitude of Force (N)
- Direction of Force

4. **Bottom Segment of the Wire**:
- Magnitude of Force (N)
- Direction of Force

5. **Net Torque**:
- Find the magnitude of the net torque on the loop about the axle.

### HINT
- Use the formula for the magnetic force on a current-carrying wire segment in a uniform magnetic field: \( \mathbf{F} = I

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