8.3 Electric Force

8.3 Electric Force

Measuring Charge and Electric Force

What is Charge? 🔆

Charge is a fundamental property of matter, similar to mass, physical state, or density.

• Neutral Atoms: Equal numbers of protons (positive charge) and electrons (negative charge) result in a net charge of 0.

• Charged Atoms: Atoms become charged when electrons are added or removed:

  • Negative Charge: Gained electrons.

  • Positive Charge: Lost electrons.

Charge is entirely dependent on the movement of electrons.

How Do Things Become Charged? 🚗

There are two types of charge:

• Positive Charge: Occurs when electrons are removed.

• Negative Charge: Occurs when electrons are added.

Interactions:

• Opposites Attract: Positive and negative charges attract each other.

• Like Charges Repel: Two positive or two negative charges repel each other.

Dipoles: Even without changing the electron count, the arrangement of charges can create regions of partial charge. This separation of positive and negative charges within an object is referred to as a dipole.

Measuring Charge 🎛

• Unit of Measurement: Coulombs (C).

• Elementary Charge (e): The charge of one electron: .

• Charges in atoms are always integer multiples of :

  • Example: Removing 3 electrons gives a charge of .

Point Charges: Charged particles are often referred to as “point charges” when their charge is concentrated at a single point.

Electric Force 🔋

When two charges are near each other, they exert a force on one another that can be either:

• Attractive: Opposite charges.

• Repulsive: Like charges.

Coulomb’s Law:

The magnitude of the electric force between two point charges is given by:

Where:

• : Electric force (N).

• : Charges (C).

• : Distance between charges (m).

• : Coulomb’s constant .

Relationships:

• Inverse Proportionality: Force decreases as distance increases.

• Direct Proportionality: Force increases with greater charge magnitudes.

Coulomb’s Law Example 🔌

Problem:

• Atom 1: Gains one extra electron.

• Atom 2: Loses one electron.

• Distance: 0.5 m.

• Find the force between them.

Solution:

1. Identify variables:

   • , , .

2. Plug into Coulomb’s Law:

3. Solve:

Result: Each particle experiences an attractive force of .

Superposition Principle ➕

When multiple electric forces act on a charge, their net force can be found by:

• Adding Forces as Vectors: Treat forces as vectors to calculate the net force.

Example:

• Charges: Atoms 1 and 2 are positive, Atom 3 is negative.

• Forces:

  • Atom 2 repels Atom 1 to the right.

  • Atom 3 attracts Atom 1 to the right.

• Net Force: Sum of forces from Atoms 2 and 3 results in a net force to the right.

Net Forces at an Angle 💡

For forces acting at angles:

1. Break into Components:

   • Find x and y components of each force.

2. Find Net Force:

   • Add x components and y components separately.

   • Use the Pythagorean theorem to find the total force.

3. Determine Direction:

   • Use trigonometry to find the angle of the net force.

Practice Problems! ❔

Use Coulomb’s law and vector addition to solve these:

1. Electron Flow: 4.16 electrons move through a wire. How many Coulombs of charge were moved?

2. Attractive Force: A sock with of charge and a carpet with are 0.500 m apart. Find the electric force.

3. Net Force: Given:

   • at (0, -3).

   • at (3, 0).

   • at (0, 2).

   • Find the net force on .