Goal to understand what electric force is and how to calculate it
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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

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Goal to understand what electric force is and how to calculate it

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.


Yesterday
Yesterday: calculate it.

  • 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?


Ball downhill
Ball downhill calculate it.

  • 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).


Now for the math
Now for the math calculate it.

  • 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.


If we add in e
If we add in E calculate it.

  • 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.


Using the vectors
Using the vectors calculate it.

  • 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.


2 dimensions
2 dimensions calculate it.

  • 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?


Now we take the next step
Now we take the next step calculate it.

  • 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?


Field lines
Field lines calculate it.

  • 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)


Motions of a charge in a uniform electric field
Motions of a charge in a uniform electric field calculate it.

  • 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


Motions of a charge in a uniform electric field1
Motions of a charge in a uniform electric field calculate it.

  • 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.


Conclusion
Conclusion calculate it.

  • 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.


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