Unit 7: Magnetic Force and Field Lesson 7.3 Magnetic Flux

Unit 7: Magnetic Force and Field

Lesson 7.3: Magnetic Flux

Contents

  • Introduction

  • Learning Objectives

  • Warm Up

  • Learn About It!

  • Magnetic Flux

  • Magnetic Flux Through an Open Surface

  • Gauss’s Law for Magnetism

  • Key Points

  • Key Formula

  • Check Your Understanding

  • Challenge Yourself

  • Bibliography

  • Key to Try It!

Introduction

  • Importance of Compass: A compass is vital for determining the direction of the magnetic field.

  • Historical Discovery: In 1993, two scientists discovered that European robins have inherent magnetoreception, the ability to perceive magnetic fields.

  • Other Species: This ability is also present in turtles, bats, butterflies, fish, and some bacteria, explaining their navigation abilities over long distances.

  • Lesson Focus: This lesson covers the relationship between the magnetic field and the concept of magnetic flux.

Learning Objectives

  • By the end of this lesson, you should be able to:

    • Explain the concept of magnetic flux.

    • Solve the magnetic flux through a given open surface.

    • State Gauss’s Law for Magnetism.

  • Competencies:

    • Evaluate total magnetic flux through an open surface (STEM_GP12EMIIh-55).

    • Explain why the magnetic flux on a closed surface is zero (STEM_GP12EMIIh-56).

Warm Up: Magnetic Flux

  • Duration: 5 minutes

  • Materials Needed: Laptop/tablet/computer, pen, and sheet of paper.

  • Procedure:

    1. Access the animation showing a rotating rectangular loop (link provided).

    2. Pause at specified timestamps and record observations in Table 7.3.1.

Learn About It!

  • Magnetic Field Lines: Show the magnitude and direction of the magnetic field from a moving charge.

  • Definition of Magnetic Flux: The measurement of the number of magnetic field lines passing through a surface area. It is related to the concept of electric flux previously studied using Gauss’s Law.

  • SI Unit of Magnetic Flux: Weber (Wb)

    • Equivalent to 1 volt per second.

  • Measurement of Magnetic Field: Tesla (T)

    • Equivalent to 1 newton per second or 1 coulomb per meter.

  • Conversion: 1 Wb/m² = 1 T.

Magnetic Flux Through an Open Surface

  • Setup: Consider a flat surface with area A, at angle θ with respect to the magnetic field vector.

    • Maximum magnetic flux occurs when θ = 0.

  • Mathematical Representation:

    • The total magnetic flux through a surface can be represented mathematically as:

ext{Magnetic Flux} = ext{Σ }(B imes A imes ext{cos}( heta))

  • Where

    • ext{Φ} = Total magnetic flux through the surface

    • B = Magnitude of the magnetic field

    • A = Area of surface

    • heta = Angle between the magnetic field and the normal to the surface.

  • Alternatively represented as:

ext{Φ} = B imes A imes ext{cos}( heta)

Gauss’s Law for Magnetism

  • Understanding Magnetic Dipoles: For a closed surface around a magnetic dipole, equal flux flows in and out, creating closed, continuous loops of field lines.

  • Key Concept: Unlike electric charges, magnetic dipoles always have zero net magnetic flux because:

ext{Total Magnetic Flux} = 0

  • Mathematical Representation of Gauss’s Law:

    • ext{Φ} = ext{∮ B•dA} = 0 where the integral denotes the closed surface integral of the magnetic field.

Examples and Practice Problems

  • Example 1: Solving for the magnetic flux through a loop.

    • Given: Area = 6 imes 10^{-4} m^2 and magnetic field B = 0.3 T (perpendicular, thus heta = 0)

    • Calculation:

ext{Φ} = B imes A imes ext{cos}(0) = 0.3 imes 6 imes 10^{-4} = 1.8 imes 10^{-4} Wb

  • Try It!: Modify area and magnetic field, calculate for different known values.

  • Example 2: For an antenna with calculation of angles and magnetic flux.

    • Known Values: Area = 2.5 m^2, Inclination = 52^ ext{o}, B = 50000 nT (nanotesla).

    • Steps:

    • Calculate angle between normal and B vector as 38^ ext{o}.

    • Magnetic Flux: 9.85 imes 10^{-5} Wb.

Key Points

  • Definition of Magnetic Flux: Number of magnetic field lines through a surface.

  • Unit of Measurement: Weber (Wb), equivalent to 1 volt per second.

  • Key Property: Total magnetic flux in an open surface is the sum of contributions from area elements.

  • Gauss’s Law for Magnetism: Total magnetic flux through a closed surface is zero.

Key Formula

  • Magnetic Flux through an Open Surface:

ext{Φ} = B imes A imes ext{cos}( heta)

Check Your Understanding

  • True/False Statements: Evaluate various assertions regarding magnetic flux and magnetic fields.

Challenge Yourself

  • Conceptual and mathematical challenges regarding magnetic flux and surface orientation.

Bibliography

  • References to various physics textbooks for further reading.

Key to Try It!

  • Correct answers for practice problems provided for self-assessment.