lesson 24.2 notes ppt and solving (1)

Page 1: Introduction to Magnetic Fields

Overview

• Chapter 24: Magnetic Fields

• Lesson 2: Applying Magnetic Forces

Page 2: Forces on Current-Carrying Wires

Key Concepts

• Magnetic Field Interaction: When a magnet is placed in a magnetic field, it can move.

• Faraday's Discovery: A magnetic field produces a force on a current-carrying wire at a right angle/perpendicular to both the magnetic field and the current direction.

• Direction of Force: Use the right-hand rule (3):

  • Fingers: Direction of magnetic field

  • Thumb: Direction of conventional current

  • Palm: Direction of force

Page 3: Magnetic Force on Current-Carrying Wire

Force Equation

• Formula: F = I L B (sin θ)

  • Units: Magnetic field (B) in Tesla (T), where 1 T = 1 N/(A·m)

• Angle Impact:

  • sin θ = 0 (No force when parallel)

  • sin 90 = 1 (Maximum force when perpendicular)

Page 4: Earbuds and Sound Waves

Mechanism in Earbuds.

• Components: power source, magnet, and current. carrying wire

• Current Directions: Music player's current changes direction rapidly, causing the coil to vibrate.

• Sound Production: The coil's movement produces sound waves due to vibrations of the cone.

• steps: sources, then the magnet does a force on the current carying wire causing it to move. The wire moves into the cone and vibrates it, which produces sound energy. switch the current to keep the coil moving up and down.

• PURPOSE: convert electricity into sound

Page 5: Galvanometers and Current Measurement

Galvanometer Basics

rotates 180

• Purpose: measure small current

• component: magnet, power source, current carrying wire

• Current Measurement: The force exerted by the magnetic field on the wire loop allows for the measurement of electric current.

• Shunt: device that has low resistance

• Diff between galvanometer and electric motor:

  1. galvanometer rotates 180, while motor 360

  2. galvanometer doesn’t switch current, while electric motor you do

• Use as Ammeter and Voltmeter:

  • Ammeter: Converts galvanometer using a shunt resistor to measure larger currents.

  • Voltmeter: Uses a high-resistance multiplier in series to measure voltage.

Page 6: Electric Motors

Functionality of an Electric Motor

rotates 360

• Purpose: Converts electrical energy into mechanical energy.

• Steps: 1 is same, 2:loop will rotate half cycle or do half rotation, 3: current is reversed so another half rotation (make it continueous)

• Purpose of split-ring commutator: A split-ring commutator reverses current direction as the armature turns, enabling continuous rotation.

Page 8: Force on a Single Charged Particle

Force Calculation

• Formula: F = q v B (sin θ)

  • q: charge

  • v: velocity

  • B: strength of magnetic field

• Force Direction: Perpendicular to both the particle's velocity and the magnetic field.

Page 9: Charged Particle Motion in Magnetic Fields

Particle Direction Control

• Use of Magnets: Helps direct a charged particle's path; they move in circular paths in synchrotron accelerators to maintain velocity perpendicular to the magnetic field.

• Example: LHC accelerates protons against a potential difference of 7.2 trillion volts.

Page 11: Example Problem 1

Magnetic Field Calculation

• Problem: Calculate the strength of a magnetic field for a wire carrying 5.0 A, with a force of 0.20 N when 0.10 m of wire is in the field.

• Solution:

  • F = B I L sin 90°

  • B = 0.2 N / (5.0 A × 0.10 m) = 0.4 T

Page 12: Right-Hand Rule Application

Force Direction Determination

• Using Right-Hand Rule: Point fingers in the magnetic field direction, thumb for the current, and palm for the force direction. Understand the significance of directionality for current and field.

Page 13: Example Problem 2

Force on Charged Particle

• Problem: Calculate the force on electrons traveling at 3.0 x 10^6 m/s in a 4.0 x 10^-2 T magnetic field at right angles.

• Solution:

  • F = q v B sin 90°

  • F = (1.6 x 10^-19 C)(3.0 x 10^6 m/s)(4.0 x 10^-2 T) = 1.92 x 10^-4 N

Page 14: Direction of Force

Force Orientation

• Illustration of Force Direction: Describes a scenario where the force direction is downward.

Page 15: Magnetic Field Strength Example Problems

Multiple Scenarios

• Various Calculations: Problems calculating forces with specified currents, lengths, and magnetic field strengths. Considers different angles for current and field interactions.

Page 16: Electric Motor and Galvanometer Comparison

Functionality Similarities

• Common Mechanism: Both use a coil in a magnetic field, but the motor operates in a full 360° while the galvanometer rotates only 180°.

• Torque and Rotation: Galvanometer for current measurement vs. electric motor for mechanical energy production.

Page 17: Principles of Sound Production and Instruments

Electrical to Mechanical Energy Conversion

• Magnetic Motion Outcomes: The forces from magnetic fields cause vibrations in coils to produce sound.

• Measurement Tools: Ammeter and voltmeter uses, with definitions of shunts and multipliers provided.

Page 18: Direction and Resistance Problems

Problem Scenarios

• Analyzing problems involving wire direction in magnetic fields.

• Calculating current required given specified conditions.

Page 19: Galvanometer Performance as Voltmeter

Required Resistance Calculations

• To ensure proper deflection during measurements based on known current and voltage levels:

  1. Total resistance necessary for specified voltages versus galvanometer capacity.

Page 20: Magnetic Force Recap

Key Equations and Parameters

• F = I L B sin θ

• F = Bvq sin θ

Page 21: Magnetic Force Summary

Summary of Definitions

• Definitions of forces related to current, length, magnetic fields, and Tesla units.

• Magnetic Force (F): The force experienced by a charged particle or current-carrying wire within a magnetic field, described by the equations F = I L B sin θ for wires, and F = Bvq sin θ for charged particles.

• Current (I): The flow of electric charge measured in Amperes (A).

• Length (L): The length of the wire segment that is within the magnetic field, measured in meters (m).

• Magnetic Field (B): A field produced by magnets or electric currents, measured in Teslas (T).

• Tesla (T): The SI unit of magnetic field strength, also = N/A.m

Page 22: Galvanometer Functionality Overview

Application Scenarios

• Galvanometer Basics: A galvanometer measures small currents, it rotates 180.

• Configurations: Galvanometers can be configured in series with other components to function as ammeters and voltmeters:

  • Ammeter: Measures current by providing a low-resistance path so the majority of current flows through the galvanometer without risking damage. (connected in parallel)

  • Voltmeter: Measures voltage by including a high-resistance multiplier in series to limit the current through the galvanometer.

Page 23: Electric Motor Foundations

Armature Dynamics

• Highlights the function of the armature in electric motors and its ability to rotate, converting electrical energy into mechanica energy.

• Armature Dynamics:

  • The armature is a crucial component that rotates in a magnetic field, converting electrical energy into mechanical energy.

  • The rotation occurs due to the interaction between the current-carrying conductors in the magnetic field, influenced by the right-hand rule.