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### Chapter 17

Electric Forces & Fields

Terms to Know

- Electrostatics: Study of electric charge
- Charged object: has unequal #s of protons and electrons
- positively charged object
- negatively charged object

- Opposite charges: attract
- + and –

- Like charges: repel
- the same charge: + and +, or – and –

- Induction: to charge an object without touching it
- Inducing by a Positive Charge
- Induction by a Negative Object

Coulomb charges

- Unit of charge: C = coulomb
- 1 proton = 1.602×10-19 C; 1 electron = ‒1.602×10-19 C

- 1 C = charge of 6.24×1018 electrons or protons

Coulomb’s Law charges

- Coulomb's Law (4 min)
- the force, F, between two charged particles, qAand qB over a distance r
- Called electrostatic force
- Mutual attraction/repulsion
- Notations: FAB= force of A exerting on B
FBA = force of B exerting on A

- |FAB | = | FBA |

- Notations: FAB= force of A exerting on B
- A vector: has a magnitude and a direction

Electrostatic Force = Coulomb’s Law charges

- Magnitude:
F = electrostatic force

kc = Coulomb constant = 8.99×109 N· m2/C2

qA = the charge of particle A

qB = the charge of particle B

r = the distance between A and B

- Analogous to Universal Law of Gravitation:
G = 6.67×10‒11 N·m2/kg2

Know that.... charges

- Coulomb’s law allows us to
- determine the magnitude of the force between two charged particles
- determine if the two charges are attracting (positive F value) or repelling (negative F value)

- Coulomb’s law doesn’t tell to which direction a particle is moving
- Must be done “manually”

Example charges

- qA = +3 C located at +1 m from the origin and qB = -2 C located at -2m.
- The negative F = Particles A and B are attracting
- The particle A moves to left; B moves to right
- How do we express the directions?
- Don’t use a sign for attraction or repulsion
- Use the signs to indicate the directions of force (N=+; S= ‒, etc)

- How do we express the directions?

Problem-Solving Strategy charges

- Drawing always helps
- Indicate the direction of force
- Use the signs for the directions of F, not for the charges of particles
- Vectors are algebraically additive if they lie in the same dimension (Principal of superposition)
- Use Trig functions to break down a vector to x- and y- component

- Use the Coulomb’s law to get the magnitude of the force
- Consider if the answer is reasonable

Sample Problem, Pg 17A, Pg 635 charges

The electron and proton of a hydrogen atom are separated, on average, by a distance of 5.3×10−11 m. Find the magnitude of the electric force and the gravitational force that each particle exerts on the other.

To get the resultant force on a particle charges

- Identify all forces acting on the particle
- Don’t include the forces the particle exerting on other particles
(Ex)

- Don’t include the forces the particle exerting on other particles
- Resolve each force into x- and y-component
- Get the sum of each component
- Using the Pythagorean theorem, get the hypotenuse, which is the resultant force

Example 17B, Pg 638 charges

Consider three point charges at the corners of a triangle, as shown right, where q1=6.00×10-9 C, q2=-2.00×10-9 C,

and q3=5.00×10-9 C. Find the magnitude and

direction of the resultant force on q3.

Example Problem 2 charges

- A charged particle, A (+6.0 μC) is located near another charged particle B (-3.0 μC) and is located 4.0 cm from the right of A.
- What is the force of B on A?

(b) A third particle (+1.5 chargesμC) is added to the configuration. If it is located 3.0 cm directly beneath A, what is the new net force on A?

Equilibrium charges

- the state in which the net force = 0
- Must have at least three charged particles
- Must have two opposite forces with the same magnitude for the center particle
(Ex) (1) + - + (2) - + -

(3) - - - (4) + + +

- is seen as objects at rest or at constant velocity

Sample Problem charges17C, Pg 640

Three charges lie along the x-axis. One positive charge, q1 = 15 µC, is at x = 2.0 m, and another positive charge, q2=6.0 µC, is at the origin. At what point on the x-axis must a negative charge, q3, be placed so that the resultant force on it (q3) is zero.

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