PHY 303L Test 1 Review

Conductors and Electric Fields

Electrons on the surface of a conductor are not bound to specific atoms, allowing for their free movement.
In the absence of an external electric field, these conduction electrons can move throughout the conductor without constraints.

The electric field within a conductor is zero when in a static state, meaning there is no movement of charges.
If there were any internal charge present, it would create a disturbance in the flow of current, resulting in a non-zero electric field inside the conductor; therefore, it is effectively shielded from internal electric fields.

Every point on the surface of a conductor is maintained at the same electric potential, which is crucial for the equilibrium of the conductor.
The potential difference between any two points on the surface, such as point A and point B, is zero, meaning there is no voltage difference which helps prevent the formation of electric fields inside the conductor.

Electric field lines around conductors are always drawn perpendicular to the surface at every point, representing the direction of the electric force.
The density of these lines indicates the strength of the electric field: closer lines signify a stronger field.

Electric forces are the interactions between charged particles, which depend on the magnitude of their charges and the distance separating them.
This force is represented as a vector, possessing both a magnitude (the strength of the force) and a direction determined by the nature of the charges involved.
It is essential to consider net forces, calculating the components separately in both the x and y axes to understand the complete effect of multiple forces acting on a charge.

Coulomb's Law mathematically describes the interaction between two point charges and is expressed as:
[ F = k \frac{|q_1 \cdot q_2|}{r^2} ]
Where:
- ( F ) is the magnitude of the force between the charges,
- ( k ) is Coulomb's constant (approximately ( 8.99 \times 10^9 \ N \cdot m^2/C^2 )),
- ( q_1 ) and ( q_2 ) are the magnitudes of the charges, and
- ( r ) is the distance between the centers of the two charges.
Notably, the force is inversely proportional to the square of the distance (( r^2 )), indicating that as the distance increases, the force decreases rapidly.

Objects with like charges will repel each other, while objects with opposite charges will attract one another, which is fundamental to understanding electrostatic interactions.

When a negatively charged balloon is brought near a neutral conducting wall, it induces a separation of charges within the wall.
The negative charges in the wall are repelled away from the balloon, leaving a net positive charge closer to the surface of the balloon, creating an attractive force.

If the negatively charged balloon directly touches the conducting wall, electrons can transfer, neutralizing the left side of the wall and allowing for a redistribution of charge within the wall.
Conversely, with an insulator, no charge transfer occurs, and instead, the balloon would remain stuck to the wall due to the induced charges.

Charging by induction is a method that uses an external charged object to separate charges within a neutral object without any direct contact between them.

When a positively charged rod is brought near two touching, neutral spheres, the charges within the spheres rearrange: the left sphere gains negative charge due to attraction to the rod, while the right sphere becomes positively charged.
After removing the rod and separating the spheres, they retain their respective induced charges, demonstrating permanent charge separation through induction.

To solve for the force between two or more charges, it’s essential to consider the coordinates of individual components, breaking down forces into x and y components.
For example, if calculating the net force acting on a charge involves multiple charges situated at different angles, each force must be individually assessed and summed to identify the overall effect.

When charges are oriented in various directions, the forces must be resolved into their components using trigonometric relationships (sine and cosine functions), as this helps determine the resultant vector from the individual forces, which indicates the total force acting on the charge.

In summary, positive charges repel each other while negative charges attract, guiding the interactions between charged objects. This fundamental rule significantly influences the resultant force's magnitude and direction in any charge interaction.