Magnetic Forces Lab

Lab 4: Magnetic Forces

• The objective is to investigate the force on a current-carrying wire in a magnetic field
• The investigation verifies its dependence on the magnitude and direction of the current and magnetic field
• The experiment measures the magnetic field of a permanent magnet using a current balance.

Prelab

• Review relevant sections in Serway, chs. 29.1, 29.2, and 29.6
• Derive the expression for $B$ as a function of $I$ and $F/L$
• Sketch the magnetic field for configuration 1, where the magnet is oriented perpendicular to the wire
• Sketch the magnetic field for configuration 2, where the magnet is oriented parallel to the wire
• Error analysis should be considered.

Introduction: Force on a Wire

• A magnetic field exerts a force on a moving charge.
• When a wire carries a current, charges are moving and subject to a force from the magnetic field.
• The force on a straight wire of length $L$ carrying a current $I$ in a magnetic field $B$ is $\vec{F} = I \vec{L} \times \vec{B}$
• The direction of $\vec{L}$ is along the wire in the direction of the current.
• Force on the wire is measured as a function of the current to determine the magnitude of the magnetic field of a magnet
• It is easier to plot Force/Length vs. Current because the length in the magnetic field cannot be easily measured
• The equation to plot is, $\frac{F}{L} = IB$
• Measuring force, length, and current makes it possible to determine the magnetic field.

The Experiment: Current Balance

• The central piece of equipment in this experiment is the current balance
• The current balance is a device that measures the force on a current-carrying wire in a magnetic field
• The current balance consists of a horizontal beam with a coil of wire suspended between the poles of a permanent magnet
• When current flows through the coil, the magnetic field exerts a force on the wire, causing the beam to deflect
• An optical sensor measures the deflection
• It is possible to determine the strength of the magnetic field by measuring the deflection as a function of current

Configurations

• Configuration 1 has the magnet oriented such that the magnetic field is perpendicular to the wire.
• Configuration 2 has the magnet oriented such that the magnetic field is parallel to the wire.

Part 1: Dependence on Current

• Set up the current balance with the magnet in configuration 1.
• Connect the power supply to the current balance and adjust the current to a desired value.
• Measure the force on the wire using the optical sensor.
• Repeat steps 2 and 3 for several different values of the current.
• Plot the force as a function of current.
• Fit a straight line to the data and determine the slope.
• From the slope, determine the magnetic field $B$.
• Repeat the procedure for configuration 2.

Part 2: Dependence on Length

• Set up the current balance with the magnet in configuration 1
• Connect the power supply to the current balance and adjust the current to a desired value
• Measure the force on the wire using the optical sensor
• Repeat steps 2 and 3 for different lengths of the wire by using different coils
• Plot the force as a function of length
• Fit a straight line to the data and determine the slope
• From the slope, determine the magnetic field $B$

Part 3: Measuring an Unknown Field

• Set up the current balance with the unknown magnet.
• Connect the power supply to the current balance and adjust the current to a desired value.
• Measure the force on the wire using the optical sensor.
• Repeat steps 2 and 3 for several different values of the current.
• Plot the force as a function of current.
• Fit a straight line to the data and determine the slope.
• From the slope, determine the magnetic field $B$.
• Compare your result to the known value of the magnetic field of the magnet.

Error Analysis

• Estimate the uncertainties in your measurements of the current, length, and force.
• Use error propagation to determine the uncertainty in your determination of the magnetic field $B$.
• Compare your measured value of the magnetic field to the known value and determine if they agree within the experimental uncertainty.

Questions

• How does the force on a current-carrying wire in a magnetic field depend on the magnitude of the current?
• How does the force on a current-carrying wire in a magnetic field depend on the direction of the current?
• How does the force on a current-carrying wire in a magnetic field depend on the magnitude of the magnetic field?
• How does the force on a current-carrying wire in a magnetic field depend on the direction of the magnetic field?
• How does the force on a current-carrying wire in a magnetic field depend on the length of the wire?
• What are the sources of error in this experiment?
• How could you improve the accuracy of this experiment?

Heat Transfer in Buildings

• Focuses on the movement of energy
• Essential for designing efficient building systems

Introduction

• Heat flow transfers energy from one body to another due to a temperature difference
• Thermodynamics involves the amount of heat transfer as a system undergoes a process from one equilibrium state to another
• Heat transfer deals with the rates of such energy transfers
• Energy transfers as heat moving from high to low temperature, ceasing when both mediums reach the same temperature

Modes of Heat Transfer

• Conduction, Convection and Radiation

Conduction

• Transfer of energy from more energetic particles to adjacent less energetic ones due to interactions
• Takes place in solids, liquids, or gases
• Relies on collisions and diffusion of molecules during random motion in gases and liquids
• Depends on vibrations of molecules in a lattice and energy transport by free electrons in solids

Rate of Heat Conduction

• $\dot{Q}_{\text {cond }}=-k A \frac{d T}{d x} \quad(W)$ (W)
• $k$ is the thermal conductivity of the material
• $A$ is the area normal to the direction of heat transfer
• $dT/dx$ is the temperature gradient (K/m or °C/m)

Thermal Conductivity

• Measures the ability of a material to conduct heat

Thermal Resistance

• $R=\frac{L}{k}$
• $L$ is the thickness of the material

Convection

• Mode of energy transfer between a solid surface and adjacent liquid or gas in motion, involving combined conduction and fluid motion
• Faster the fluid motion, the greater the convection heat transfer
• Heat transfer is by pure conduction without bulk fluid motion

Forced Convection

• Fluid is forced to flow over the surface by external means like a fan, pump, or wind

Natural (or free) convection

• Fluid motion caused by buoyancy forces induced by density differences due to temperature variation

Rate of Heat Convection

• $\dot{Q}{\text {conv }}=h A\left(T{s}-T_{\infty}\right) \quad(W)$
• $h$ is the convection heat transfer coefficient
• $A$ is the surface area
• $T_s$ is the surface temperature
• $T_\infty$ is the fluid temperature far from the surface

Radiation

• Energy emitted by matter as electromagnetic waves or photons due to changes in electronic configurations
• Transfer does not need an intervening medium
• Fastest method
• Suffers no attenuation in a vacuum
• A volumetric phenomenon

Blackbody Radiation

• The maximum radiation rate emitted from a surface at a temperature $T_s$:
• $\dot{Q}{\text {emit, max }}=\sigma A{s} T_{s}^{4} \quad(W)$

Emissivity

• Measure of how closely a surface approximates a blackbody, where $\epsilon = 1$

Rate of Radiation Emitted by a Real Surface

• $\dot{Q}{\text {emit }}=\varepsilon \sigma A{s} T_{s}^{4} \quad(W)$
• $\epsilon$ is the emissivity of the surface
• $\sigma = 5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}^{4}$ is the Stefan-Boltzmann constant
• $A_s$ is the surface area
• $T_s$ is the surface temperature

Absorptivity

• The fraction of radiation energy incident on a surface that is absorbed

Rate at Which a Surface Absorbs Radiation

• $\dot{Q}{\text {abs }}=\alpha \dot{Q}{\text {incident }} \quad(W)$
• $\alpha$ is the absorptivity of the surface
• $\dot{Q}_{\text {incident }}$ is the rate at which radiation is incident on the surface

Net Radiation Heat Transfer

• $\dot{Q}{\text {rad }}=\varepsilon \sigma A{s}\left(T_{s}^{4}-T_{\text {surr }}^{4}\right) \quad(W)$
• $A_s$ is the surface area
• $T_s$ is the surface temperature
• $T_{surr}$ is the average temperature of the surfaces surrounding the surface
• $T_s$ and $T_{surr}$ must be in $K$ or $R$

Simultaneous Heat Transfer

• Total conductive heat transfer: $\dot{Q}=\dot{Q}_{\text {cond }}$
• Total heat transfer is: $\dot{Q}=\dot{Q}{\text {conv, 1}}=\dot{Q}{\text {cood }}=\dot{Q}_{\text {conv. 2}}$
• Combined radiation and convection heat transfer: $\dot{Q}=\dot{Q}{\text {conv }}+\dot{Q}{\text {rad }}$

Understanding Your Credit Report

• A credit report is a record of your credit activity and payment history.
• Lenders, creditors, and other businesses use this report to assess your creditworthiness.

Data Providers

• Credit bureaus collect data from creditors, lenders, and public records to create credit reports.

Information Included

• Personal Information: Name, address, date of birth, Social Security number, and employment history.
• Credit Accounts: Information about your credit cards, loans, and other lines of credit, including account numbers, credit limits, balances, payment history, and account status.
• Public Records: Bankruptcies, foreclosures, tax liens, and judgments.
• Inquiries: A list of companies that have accessed your credit report.

Importance of Credit Report

Your credit report plays a significant role in your financial life, affecting your ability to:

• Obtain credit cards, loans, and mortgages.
• Get approved for rental housing.
• Secure insurance coverage.
• Get hired for certain jobs.

Credit Bureaus

• Equifax: www.equifax.com, 1-800-685-1111
• Experian: www.experian.com, 1-888-397-3742
• TransUnion: www.transunion.com, 1-800-916-8800

Understanding Your Credit Score

• A credit score is a three-digit number summarizing your creditworthiness based on the information in your credit report.
• It is used by lenders and creditors to assess the risk of lending you money.

Credit Score Calculation

• Credit scores are calculated using mathematical algorithms that evaluate various factors in your credit report.
• The most common credit scoring model is FICO.

Factors Affecting Credit Score

• Payment History (35%): Paying your bills on time is the most important factor.
• Amounts Owed (30%): The amount of debt you owe compared to your credit limits.
• Length of Credit History (15%): The age of your oldest and newest credit accounts, and the average age of all your accounts.
• Credit Mix (10%): Having a variety of credit accounts, such as credit cards, loans, and mortgages.
• New Credit (10%): Opening too many new accounts in a short period can lower your score.

Credit Score Ranges

Free Credit Report

• You're entitled to a free copy of your credit report from each of the three major credit bureaus every 12 months.
• Website: www.annualcreditreport.com

Disputing Errors

• If you find any errors on your credit report, you have the right to dispute them with the credit bureau and the creditor that reported the information.

Steps to Dispute Errors

1. Gather Documentation: Collect any documents that support your dispute.
2. Write a Dispute Letter: Explain the error and provide supporting documentation.
3. Send the Dispute Letter: Send your dispute letter to the credit bureau via certified mail.
4. Follow Up: The credit bureau has 30 days to investigate your dispute.
5. Review Results: The credit bureau will notify you of the results, which will correct any errors.

Sample Dispute Letter

• Include: Creditor info, Account number and explanation of why the information is incorrect

Tips for Improving Your Credit Score

• Pay Bills on Time: Set up reminders or automatic payments.
• Reduce Credit Card Balances: Aim to keep your credit card balances below 30% of your credit limit.
• Monitor Your Credit Report: Check your credit report regularly for errors.
• Become an Authorized User: Ask to become an authorized user on a well-managed credit card.

Additional Resources

• Federal Trade Commission (FTC): www.ftc.gov
• Consumer Financial Protection Bureau (CFPB): www.consumerfinance.gov
• National Foundation for Credit Counseling (NFCC): www.nfcc.org

Bernoulli's Principle

• Increase in fluid speed occurs simultaneously with decrease in pressure or potential energy

Demonstration

• Hold two pieces of paper a few inches apart and blow air between them.
• The papers will move closer together due to the fast-moving air having lower pressure.

Bernoulli's Equation

• $P + 1/2 \rho v^2 + \rho gy =$ Constant
• $P$ = absolute pressure of the fluid
• $\rho$ = fluid density
• $v$ = fluid velocity
• $g$ = acceleration due to gravity
• $y$ = height

Example

• If water comes out of a faucet with a speed of 3 m/s, what is the pressure at a point 10 cm below the faucet?

Solution

• $P_1 + 1/2 \rho v_1^2 + \rho gy_1 = P_2 + 1/2 \rho v_2^2 + \rho gy_2$
• $P_1 = P_0$
• $y_1 = 0$
• $v_1 = 3 m/s$
• $y_2 = 0.1 m$
• $v_2 = 3 m/s$
• $P_0 + 1/2 \rho v_1^2 + 0 = P_2 + 1/2 \rho v_2^2 + \rho gy_2$
• $P_2 = P_0 - \rho gy_2 = 1.0 * 10^5 - (1000)(9.8)(0.1) = 98100 Pa$

Relación señal a ruido (SNR)

Definición:

• La SNR compara la potencia de una señal deseada con la potencia del ruido de fondo.
• Una SNR más alta indica que la señal es más fuerte en comparación con el ruido.

Cálculo:

• Fórmula: $SNR = \frac{P_{señal}}{P_{ruido}}$
  • $P_{señal}$: Potencia de la señal.
  • $P_{ruido}$: Potencia del ruido.
• En decibelios (dB): $SNR(dB) = 10 \log_{10}(\frac{P_{señal}}{P_{ruido}})$

Ejemplo:

• Si la potencia de la señal es 100 y la del ruido es 1:
  • $SNR = \frac{100}{1} = 100$
  • En dB: $SNR(dB) = 10 \log_{10}(100) = 20 dB$

Interpretación:

• Una SNR de 20 dB implica que la señal es 100 veces más potente que el ruido.
• Valores más altos de SNR indican una mejor calidad de la señal.
• Utilizado en el procesamiento de imágenes para medir la calidad, donde una SNR alta denota poco ruido y claridad en la imagen.