Potential Gradients

Question 1

What is an equipotential surface?

Answer 1

A surface for which tow potentials at different points are the same
Va=Vb

Question 2

How are the electric field lines related to an equipitential?

Answer 2

The field lines are always perpendicular to the equipotential surface

Question 3

What is the gradient of a potential in 3D?

Answer 3

dV=-Ex dx -Ey dy -Ez dz
dV(x, y,z) =∂V/∂x dx +∂V/∂y dy +∂V/∂z dz

Question 4

How do the electric field and potential relate?

Answer 4

⃗E=− ∂V/∂x x(hat)̂− ∂V/∂y y(hat)̂− ∂V/∂z z(hat)̂
≡− ∇ V