Goal: To understand what electric force is and how to calculate it.

1. Goal: To understand what electric force is and how to calculate it. Objectives: Understanding how to translate electric field to force Understand how to calculate Electric forces Knowing what Electric Field lines are and how to use them Understanding motions of a charged particle in a constant electric field.

2. Yesterday: • We learned that the Electric field is a topography of electric charges around you. • At any point the electric field is just a sum of the topography from each charge. • For each charge E = -qk / r2 • How would this translate to a force?

3. Ball downhill • If you have a gravitational topography a ball will want to roll downhill. • That is it will roll from a high elevation to a low one or a high field to a low one. • The same is true of electric fields. • A positive charge will want to move to a lower electric field. • A negative charge will do the opposite and will want to move up to a higher valued electric field (moving uphill).

4. Now for the math • The force on a charge is: • F = E * qon • Where qon is the charge the force is being applied to and E is the electric field that charge qon is located at. • Much like for gravity that F = m * g on the surface of the earth.

5. If we add in E • If we have 2 charges called qon and qby then the force is: • F = qon * E, but E = -qby k / r2 • So, F = -qon * qby * k / r2 • (k is the same constant we had before) • And if there are more than 2 charges, each charge will have a force on qon. • The net force will add up just like you add them up for E.

6. Using the vectors • The vector way to find the force: • Fx = -k qon * qby * x / r3 (x hat) • Fy = -k qon * qby * y / r3 (y hat) • Sanity check: like charges repel and opposites attract. The sign and direction should reflect that.

7. 2 dimensions • Just like yesterday in 2 dimensions you have to take the dimensions into account. • We will start off with a straightforward 3 charge problem. • q2 = 5 C and is at y = 3, X = 0 • q3 = 9 C and is located at y = 0, x = 6 • What is the total force on q1 if it is at the origin and has charge of 3 C?

8. Now we take the next step • Now a little bit harder. • q2 = 3 C is at y = -2, x=0 • q3 = -5 C and is at x = 3, y = -4 • q1 = -2 C and is at the origin • What is the vector form of the force and what is the magnitude of the force on q1?

9. Field lines • Another way to look at this is by looking at field lines. • Field lines point downhill – the direction a positive charge will flow. • While these lines will tend to move towards – charges and away from + charges, that is not always the case if you have many charges. • (draw on board)

10. Motions of a charge in a uniform electric field • Imagine you have an entire room where at any point in that room the electric field is about the same. • If you put a charge into that room then what will the charge do? • A) do nothing – no movement • B) move around in a circle • C) move around the room in random way • D) accelerate in some direction at a constant rate • E) accelerate in some direction in an ever increasing rate

11. Motions of a charge in a uniform electric field • Imagine you have an entire room where at any point in that room the electric field is about the same. • If you put a charge into that room then what will the charge do? • A) do nothing – no movement • B) move around in a circle • C) move around the room in random way • D) accelerate in some direction at a constant rate • E) accelerate in some direction in an ever increasing rate • Since F = q * E that already tells you the force will be a constant because q and E are constant here. • Also, ALWAYS remember that F = ma… • So, F = q * E = ma • So a = q * E / m for a uniform electric field! • Thus the acceleration is constant and the direction will be determined by the charge and the direction of the electric field.

12. Conclusion • F = q * E • Electric Field lines point downhill. • If E is uniform then F and a are constants! • Once again the hardest part is doing the geometry.