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. - PowerPoint PPT Presentation

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.

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:
• 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
• 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
• 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 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
• 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
• 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 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
• 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
• 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 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.
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.