ENM - Overview of 1A-1D

What is the difference between electric field and electric force?

Electric field exists in space, electric force is what a charge feels

Which exists without a test charge: electric field or electric force?

Electric field exists without a test charge

What does the equation E = −∇φ represent?

Electric field points in direction of greatest decrease of potential

What does the negative sign in E = −∇φ mean physically?

Electric field E points from high potential φ to low potential φ

When should you use E = −∇φ in a problem?

When potential is given and you need the field

When should you integrate electric field to find potential?

When field is given and you need voltage or potential difference

When should you use Gauss’s Law instead of Coulomb’s Law?

When there is strong symmetry (sphere, cylinder, infinite plane)

What condition lets you pull the field out of a Gauss’s Law integral?

Field is constant over the surface

If you see a uniformly charged sphere or infinite cylinder, what should you use?

Gauss’s Law with matching Gaussian surface

What is the electric field inside a hollow spherical shell?

Zero

Why is the field zero inside a spherical shell?

Symmetry cancels all contributions

How does the field behave inside a uniformly charged solid sphere?

Increases with distance from center

How does the field behave outside a uniformly charged solid sphere?

Acts like a point charge (1 over r squared)

Why does Gauss’s Law work best for symmetric shapes?

Field becomes constant over the surface so it simplifies the integral

Why is the field exactly zero inside a shell, not just small?

Perfect symmetry gives exact cancellation

Why does Gauss’s Law fail for irregular shapes?

Field is not constant over the surface

Why is E = −∇φ more reliable than guessing direction?

Always gives correct direction even in complex setups