1 of 26

STS.024 Midterm

Dancing our way

through Electric Fields

Montserrat Diaz Botello and Emma Martinez

2 of 26

Students should have already learned what an electric field is and that they point radially in/outwards from a -/+ charge.

Assumptions

NOTE: Our lessons focus more on conceptual understanding rather than calculations of electric fields

3 of 26

Day 1: Gauss’s Law

4 of 26

Introduction to Gauss’s Law

Gauss's Law describes how electric flux through a “Gaussian surface" (a closed surface) is equal to the net charge enclosed divided by the permittivity of free space (ε0)

​

E = Electrical Field

5 of 26

Shapes of Gaussian Surfaces

Used for slabs,

and two plates

Used for “wires” (a.k.a. cylinders) and lines

Used for

charged spheres

Cylinder�(Base sides)

Cylinder

(Lateral side)

Sphere

6 of 26

When NOT to use

Gaussian Surfaces

When the shape lacks sufficient symmetry for a cylinder or sphere; edge effects

Examples: rings, disks,

asymmetrical shapes

7 of 26

Students should spend the next lecture learning to calculate E using Gauss’s Law.

8 of 26

Dance Time!

9 of 26

Call and Response

We give you the shape of the charge distribution

Some students will form the corresponding Gaussian Surface

Some students will come together to

represent that charge distribution

10 of 26

Practice #1

​

Point Charge

+Q

Now form the corresponding Gaussian Surface!

​

  • What Gaussian Surface shape did you choose, and why?
  • Where is the normal vector?
  • What is its surface area?
  • What is the charge enclosed?

11 of 26

Practice #1

​

Point Charge

+Q

  • Sphere (spherical symmetry)
  • Surface Area: 4πr2
  • Charge Enclosed: +Q

Sphere

Normal vector

12 of 26

Practice #2

​

Wire (Cylinder)

Now form the corresponding Gaussian Surface!

​

  • What Gaussian Surface shape did you choose, and why?
  • Where is the normal vector?
  • What is its surface area?
  • What is the charge enclosed?

*Uniform charge distribution of 𝜆

13 of 26

Practice #2

​

Wire (Cylinder)

  • Cylinder (radial symmetry)
  • Surface Area: 2πrh
  • Charge Enclosed: 𝜆h

Cylinder

(Lateral Side)

Normal vector

14 of 26

Practice #3

​

Slab

Now form the corresponding Gaussian Surface!

​

  • What Gaussian Surface shape did you choose, and why?
  • What is its surface area?
  • What is the charge enclosed?

*Uniform charge distribution of 𝞺

d

15 of 26

Practice #3

​

Slab

  • Cylinder (z-axis symmetry)
  • Surface Area: πr2
  • Charge Enclosed: 𝞺πr2d

Cylinder

(Base Side)

Normal vector

16 of 26

Day 2: Electric Field Integrals

17 of 26

Students should have already learned how to take the electric field of a gaussian surface

Assumptions

NOTE: Our lessons focus more on conceptual understanding rather than calculations of electric fields

18 of 26

Introduction to the surface integral

The electric field integral method calculates the electric field produced by a continuous charge distribution. It sums up infinitely many point charges and their respective fields to get the overall electric field. 1/(4πε0) is equal to k.

19 of 26

Shapes with continuous charge distribution

Rod

Ring

Disk

20 of 26

Dance Time!

21 of 26

Instruction-based

We will tell you how to model the shape and where the electric field moves

Students follow the example

Some students will represent the object while others will represent the direction of the electric field

22 of 26

Practice #1

​

Rod (Along y-axis)

  • Electric field is split into x and y direction to reach P
  • What happens to the electric field in each direction?
  • What is the charge of the rod?
  • What is the distance from the rod to P?

*Uniform charge distribution of Q

P

L/2

x

23 of 26

Practice #1

​

Rod (Along y-axis)

  • Electric field in the - and + y-direction cancel each other out
  • Electric field is only in x-direction, inverse of distance
  • Charge: Q/L
  • Distance between: sqrt((L/2)2+x2)

*Uniform charge distribution of Q

P

x

L/2

24 of 26

Practice #2

​

Ring

  • Electric field is split into x and y direction (r and 𝚹) to reach P
  • What happens to the electric field in each direction?
  • What is the charge of the rod?
  • What is the distance from the rod to P?

*Uniform charge distribution of Q

P

R

x

25 of 26

Practice #2

​

Ring

*Uniform charge distribution of Q

P

R

x

  • Electric field in the - and + y-direction (-/+ 𝚹 dir.) cancel each other out
  • Electric field is only in x-direction, inverse of distance
  • Charge: Q/2πr
  • Distance between: sqrt(R2+x2)

26 of 26

Thank you

for dancing with us!