Sci I - Symmetry and Gauss’s Law

How does symmetry simplify modeling forces in physics?

By showing that components of forces in opposite directions can cancel out.

What is an example of symmetry with tugboats?

If two tugboats pull a ship in exactly opposite directions with the same strength, the net force is zero.

What happens if tugboats pull mostly forward but partially opposite?

The forward components add, the left/right components cancel, and the ship moves forward.

How does symmetry apply to two positive charges with a proton in between?

The proton is repelled equally by both charges, so net force is zero.

What does it mean for the electric field at the midpoint between two equal positive charges?

The net electric field is zero at that point.

If the proton is nudged slightly forward between two charges, what happens?

Forward components of the electric fields add, and the proton moves forward.

How do the horizontal components of the fields behave in this scenario?

They cancel out due to symmetry.

How do the vertical components of the fields behave when the proton moves slightly forward?

They point in the same direction and add together.

Why is symmetry useful in electric field calculations?

It allows us to ignore components that cancel out, simplifying the model.

What happens to a proton above a large, flat sheet of positive charge?

It is pushed upward by charges directly below and diagonally upward by charges off to the side.

How does symmetry affect the left/right components of the electric field from a sheet of charge?

They cancel out, leaving only the upward component.

What is the direction of the electric field from a flat sheet of charge?

Straight lines perpendicular to the sheet.

How do electric fields behave between two oppositely charged plates?

They reinforce each other, creating a uniform field.

What technique allows us to find the electric field for extended objects?

Gauss’s law.

What is Gauss’s law equation?

ϕE = q / εo

What does εo represent in Gauss’s law?

The permittivity of free space, a constant.

How is εo related to the Coulomb constant k?

εo = 1 / (4πk)

What does q represent in Gauss’s law?

The total charge contained within the Gaussian surface.

What is electric field flux (ϕE)?

A scalar quantity representing the amount of electric field passing through a given area.

How is electric field flux calculated for a uniform field?

E multiplied by the surface area A.

Give a real-world analogy for flux using rain and a bucket.

Holding a bucket upright captures more rain flux; sideways captures none; angled captures partial flux.

What happens to flux if the bucket has no bottom?

Positive flux enters through the top, negative exits through the bottom; total flux is zero.

What is a Gaussian surface?

An imagined closed geometric shape surrounding an object to calculate electric flux.

Which shape is used for a flat sheet of charge?

A cylinder.

Why does no flux pass through the sides of the Gaussian cylinder?

The sides are parallel to the electric field.

How do we calculate flux through the top and bottom of the cylinder?

Each has area A, and the flux is E*A for each.

What is the flux equation for a cylinder above a sheet of charge?

2 * E * A = q / εo

What is surface charge density σ?

The amount of charge per unit area on the sheet.

How do we express total charge in terms of σ?

q = σ * A

How do we solve for the electric field from a sheet of charge?

E = σ / (2 * εo)

Does the electric field from a sheet of charge depend on position?

No, it is constant everywhere above the sheet.

How does the field from a sheet differ from that of a point charge?

It is constant, not an inverse square law.

Why is using electric fields advantageous over calculating every particle-to-particle force?

Because we calculate the field once, instead of computing interactions between all individual charges.