1. Quiz
An electron is accelerated from rest through a potential difference V. Its final speed is proportional to:
A) V2
B) V
C) V1/2
D) 1/V

2. Electric Potential from a point charge
Equipotential surfaces and electric fields are perpendicular

3. Multiple charges q3 r3 q2 r1 r2 q1
Remember, V is not a vector, so orientation is irrelevant!

4. Quiz
Points R and T are each a distance d from each of two equal and opposite charges as shown. required to move a negative charge q from R to T is:
A) kQq / (2d)
B) kqQ / d
C) kqQ / d2
D) zero

5. Getting the Electric Field from the Potential:1D

6. Getting the Electric Field from the Potential: Vector
E is a vector, and so let’s be explicit, in Cartesian coordinates

7. Getting the Electric Field from the Potential: Vector
Therefore,
Or in unit-vector notation,

8. Vector Derivatives: Gradienmt in Cartesian Coordinates
Nambla: a vector derivative
is the gradient of V .

9. Examples:
Suppose

10. Potential and Field
Note: the field can be zero at a point, without the potential being zero.
In the middle of the ring the field is zero, however,