Unit 2.7 Electric flux

Page 1: Introduction

• Topics Covered: Electric fields, Gauss’s Law, Electric Flux

• Report By: Mutasem Jarwan, G12 ADV Physics

• Course: Electricity and Magnetism

Page 2: Learning Objectives and Performance Indicators

• Objectives:

  • Define electric flux as the quantity of electric field passing through an area A.

  • Identify area vector characteristics for flat surfaces: perpendicular and magnitude equal to surface area.

  • Divide surfaces into infinitesimal area elements with vector assignment to each.

  • Explain signs of flux: negative for inward and positive for outward.

  • Calculate net flux through a closed surface using integration of the dot product of electric field vector E and area vector dA.

  • Determine simplifications by breaking closed surfaces into parts (e.g., cube sides).

  • Solve numerical problems related to electric flux.

• Reference Textbook: Chapter 2 - Electric Field & Gauss’s Law

Page 3: Understanding Electric Flux

• Definition of Electric Flux (Φ):

  • Amount of electric field that penetrates perpendicularly through a surface.

  • Units: Nm²/C

  • Variables:

    • E: Electric Field (N/C or V/m)

    • A: Surface Area (m²)

• Flux Existence: Flux exists only if electric field lines penetrate the surface.

  • If lines enter the surface: Φ is negative.

  • If lines leave the surface: Φ is positive.

• Dot Product Considerations:

  • When electric field is parallel to surface: minimum flux.

  • When perpendicular: maximum flux.

  • When diagonal: flux is intermediate between max and min.

• Electric Flux Formula:[ \Phi_E = \int E \cdot dA = E imes A \times \cos \theta ]

Page 4: Electric Flux Variables

• Dependence on Variables: Electric flux is influenced by:

  • Magnitude of the electric field

  • Surface area

  • Angle between field direction and area vector

• Area Vector Properties:

  • Magnitude equals surface area

  • Direction is perpendicular to the surface plane.

• Cosine Factor: [ \Phi_E = E imes A imes \cos \theta ]

Page 5: Electric Flux through Different Surfaces

• Common Scenarios:

  • For a rectangle on the xy-plane with uniform electric field aligned with z-axis:

    • Electric flux: [ \Phi_E = E A \cos(0) = E_0 a b ]

    • For surfaces aligned with the xz-plane or yz-plane: [ \Phi_E = 0 ]

• Examples:

  • Determine flux values for rectangles based on orientation and electric field.

Page 6: Calculating Electric Flux with Angled Fields

• Problem 1: Given an electric field rotated to 60° with z-axis:

  • Calculate flux through a rectangle in the xy-plane: [ \Phi_E = E A \cos(60) = \frac{1}{2} E_0 a b ]

• Adjusting Angle: When angle between electric field and surface is considered:

  • New angle calculation: [ \theta = 90° - 60° = 30° ]

  • Electric flux: [ \Phi_E = E A \cos(30) = 0.86 E_0 a b ]

Page 7: Net Electric Flux in a Cube

• Net Flux Concept: Net electric flux is zero for an immersed hollow object in uniform electric field.

• Example Analysis: Electric flux through a cube oriented in an electric field:

  • Calculate flux for each face of a cube with edge length l:

    • Flux contributions from each face ( \Phi_1 = E A \cos(180°) = -E l^2 )

    • Sum of all faces yields net flux: [ \Phi_{net} = 0 ]

Page 8: Electric Flux through a Cylindrical Surface

• Cylindrical Example: Calculate net electric flux through closed cylindrical surface in a uniform electric field:

  • Identify contribution based on position in the field:

    • Basis: Field perpendicular to area (θ = 0°): [ \Phi_1 = E A = E \pi R^2 ]

    • Sides: Field parallel to area (θ = 90°): [ \Phi_2 = 0 ]

    • Total flux calculation: [ \Phi_{net} = 2\pi E R^2 ]

Page 9: Practice Question

• Engagement: Solve practice questions to reinforce understanding of electric flux concepts.