ECE 106 - Electric Potential and Potential Energy

electric potential =

work done per positive test charge as q -> 0

most general formula

V =-∞∫p E-> · dl->

why is electric potential the same regardless of the path, and which path should be taken =

E field is a conservative field, so V is same regardless of path

take straight path or along E field lines

What happens to test charge if Q is positive? Negative?

Q > 0, repulsion and positive work

Q < 0, attraction and negative work

electric potential formula for a point charge =

V = kQ/r

k = 1/4πε₀

If no Gaussian symmetry at all, how to find E-field and electric potential =

Find E-field with E = ∫(k dQ / r²) r̂

Find V_p = ∫(k dQ / r)

where k = 1 / (4πε₀)

If Gaussian symmetry exists, how to find E-field and electric potential =

Find E-field w/ Gauss Law

Find V_p = -∫(∞ to r) E dr

Potential energy change bringing charge q to a point at potential V_P =

ΔU_e = qΔV_P

Work to Potential Energy relation =

W = -ΔU_e

What is ΔV_A→B if E field IS and ISNT uniform =

V_B - V_A, opposite direction of ece 140

Uniform

kQ(1/[r_B] - 1/[r_A])

Non-uniform

-∫(∞ to B) E→ · dl→ + ∫(∞ to A) E→ · dl→ = V_B - V_A

Relation of E and V =

E→ = −∇V

E_x = −∂V/∂x, E_y = −∂V/∂y, E_z = −∂V/∂z

What is E-field in Equipotential Surfaces =

E→ is ALWAYS perpendicular to equipotential surfaces

constant V = no work is done moving a charge along one