Electric Forces Between Point Charges

Calculating the Electric Force

When multiple point charges are present, the net electric force on any one charge can be determined using Coulomb's Law and vector addition. The force between two point charges is given by:

• Coulomb's Law: The magnitude of the force between two point charges and separated by a distance is:

• Vector Addition: The net force on a charge is the vector sum of the forces exerted by all other charges.

• Example: For three charges, C at the origin, C at m, and C at m, the net force on is calculated by finding the individual forces from and and adding them as vectors.

• Worked Calculation:

  • Find the and components of each force.

  • Add the components: , .

  • Calculate the magnitude:

• Example Result: For the given configuration, the net force on is $52$ N.

The Electric Field Model

Definition and Properties

Electric fields are a fundamental concept in physics, describing the influence that electric charges exert on their surroundings.

• Electric Field (): A region of space around a charged object where other charges experience a force.

• Source Charges: Create an electric field at all points in space.

• Test Charge (): Experiences a force in the electric field:

• Direction:

  • For a positive charge, the force is in the direction of .

  • For a negative charge, the force is opposite to .

• Units: The electric field is measured in newtons per coulomb (N/C).

• Electric Field Strength: The magnitude of the electric field at a point.

Principles of Electric Force and Field

Direction and Magnitude

The direction and magnitude of electric forces and fields depend on the sign and magnitude of the charges involved.

• Like Charges Repel, Opposite Charges Attract:

  • Two positive charges or two negative charges repel each other.

  • A positive and a negative charge attract each other.

• Force Direction:

  • For a positive test charge placed in the field of another positive charge, the force is directed away from the source charge.

  • For a negative test charge, the force is directed toward the source charge.

• Electric Field Direction:

  • The electric field at a point due to a positive source charge points away from the source.

  • The electric field at a point due to a negative source charge points toward the source.

• Example: If a positive charge is at the origin and a test charge is placed at m:

  • If the test charge is positive, the force and field are in the positive direction.

  • If the test charge is negative, the force is in the negative direction, but the field remains in the positive direction.

Principle of Electric Force and Field: Quantitative Relationships

Dependence on Charge and Field

• Force Proportionality: The force between two particles is proportional to the product of their charges.

• Field Independence: The magnitude of the electric field at a point is independent of the charge of the particle used to measure it.

• Example: If two test charges of different magnitudes are placed at the same location in the field of a source charge, the force on each is proportional to its charge, but the field at that location is the same for both.

The Electric Field of a Point Charge

Mathematical Expression

The electric field created by a point charge is given by:

• : The permittivity of free space, C/(N·m).

• : The source charge.

• : The distance from the source charge to the point of interest.

• : The unit vector pointing from the source charge to the location where the field is measured.

Field Direction and Magnitude

• Positive Charge: Field lines point away from the charge.

• Negative Charge: Field lines point toward the charge.

• Magnitude: The field strength decreases with the square of the distance from the charge.

• Example:

  • At a distance from a charge, the field points radially outward.

  • At a distance from a charge, the field points radially inward.

Superposition Principle for Electric Fields

Adding Fields from Multiple Charges

When more than one charge is present, the total electric field at a point is the vector sum of the fields produced by each charge.

• Superposition Principle:

• Application: Used to find the net field at a point due to several charges.

Zero Electric Field Locations

Finding Points of Zero Field

It is possible for the electric field to be zero at certain points between two or more charges.

• Condition: The fields from each charge must be equal in magnitude and opposite in direction.

• Example: For charges and placed along a line, the field is zero at a point where the magnitudes of the fields due to each charge are equal and their directions are opposite.

• Calculation: Set and solve for the position.

Summary Table: Electric Force and Field Relationships

Additional info: These notes expand on the brief points and diagrams in the original slides, providing full academic context, definitions, and examples for each concept.