### Problem DescriptionA metal strip 5.31 cm long, 0.640 cm wide, and 0.908 mm thick moves with constant velocity through a uniform magnetic field \( B = 1.24 \text{ mT} \) directed perpendicular to the strip, as shown in the figure. A potential difference of 5.80 \( \mu \text{V} \) is measured between points \( x \) and \( y \) across the strip. Calculate the speed \( v \).### Diagram ExplanationThe provided diagram shows a rectangular metal strip moving with constant velocity \( \mathbf{v} \) upwards (indicated by a magenta arrow). The magnetic field \( \mathbf{B} \) is directed such that it points into the plane of the paper, represented by green crosses (× symbols). Points \( x \) and \( y \) are marked along the width of the strip, indicating where the potential difference is measured.### Required CalculationTo solve for the speed \( v \), use the formula derived from electromagnetic induction principles in a moving conductor within a magnetic field:\[ \epsilon = B \cdot v \cdot d \]Where:- \( \epsilon \) is the potential difference (5.80 \( \mu \text{V} \))- \( B \) is the magnetic field strength (1.24 mT)- \( v \) is the velocity of the strip (what we need to find)- \( d \) is the width of the strip (0.640 cm)Input fields for the solution (answer in the correct units):- **Number**: [Input Field]- **Units**: [Input Field; options like cm/s, m/s, etc.]Make sure to rearrange the formula to solve for \( v \):\[ v = \frac{\epsilon}{B \cdot d} \]### Example SolutionTo find the right answer, substitute values for \( \epsilon \), \( B \), and \( d \) into the formula:\[ v = \frac{5.80 \times 10^{-6} \text{ V}}{1.24 \times 10^{-3} \text{ T} \times 0.00640 \text{ m}} \]

A metal strip 5.31 cm long, 0.640 cm wide, and 0.908 mm thick moves with constant velocity through a uniform magnetic field B = 1.24 mT directed perpendicular to the strip, as shown in the figure. A potential difference of 5.80 µV is measured between points x and y across the strip. Calculate the speed v. Number Units X X X

A metal strip 5.31 cm long, 0.640 cm wide, and 0.908 mm thick moves with constant velocity through a uniform magnetic field B = 1.24 mT directed perpendicular to the strip, as shown in the figure. A potential difference of 5.80 µV is measured between points x and y across the strip. Calculate the speed v. Number Units X X X

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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### Problem Description

A metal strip 5.31 cm long, 0.640 cm wide, and 0.908 mm thick moves with constant velocity through a uniform magnetic field \( B = 1.24 \text{ mT} \) directed perpendicular to the strip, as shown in the figure. A potential difference of 5.80 \( \mu \text{V} \) is measured between points \( x \) and \( y \) across the strip. Calculate the speed \( v \).

### Diagram Explanation

The provided diagram shows a rectangular metal strip moving with constant velocity \( \mathbf{v} \) upwards (indicated by a magenta arrow). The magnetic field \( \mathbf{B} \) is directed such that it points into the plane of the paper, represented by green crosses (× symbols). Points \( x \) and \( y \) are marked along the width of the strip, indicating where the potential difference is measured.

### Required Calculation

To solve for the speed \( v \), use the formula derived from electromagnetic induction principles in a moving conductor within a magnetic field:
\[ \epsilon = B \cdot v \cdot d \]

Where:
- \( \epsilon \) is the potential difference (5.80 \( \mu \text{V} \))
- \( B \) is the magnetic field strength (1.24 mT)
- \( v \) is the velocity of the strip (what we need to find)
- \( d \) is the width of the strip (0.640 cm)

Input fields for the solution (answer in the correct units):

- **Number**: [Input Field]
- **Units**: [Input Field; options like cm/s, m/s, etc.]

Make sure to rearrange the formula to solve for \( v \):
\[ v = \frac{\epsilon}{B \cdot d} \]

### Example Solution

To find the right answer, substitute values for \( \epsilon \), \( B \), and \( d \) into the formula:

\[ v = \frac{5.80 \times 10^{-6} \text{ V}}{1.24 \times 10^{-3} \text{ T} \times 0.00640 \text{ m}} \]

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