Understanding
Coulomb's Law is pivotal when studying the interactions between charged particles. This law states that the force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance separating them. The formula is expressed as:
ewlineewline\[ F = k \frac{{|q_1 q_2|}}{{r^2}} \] where:
- \( F \) is the magnitude of the electric force between the charges,
- \( q_1 \) and \( q_2 \) are the amounts of the charges,
- \( r \) is the distance between the centers of the two charges, and
- given as \( 9 \times 10^9 \ N\cdot m^2/C^2 \), known as Coulomb's constant.
For electric field calculation, Coulomb's Law plays an essential role. The electric field \( E \) at a distance from a point charge can be derived from this law and is expressed as: \[ E = k \frac{{|q|}}{{r^2}} \] where \( q \) represents the charge creating the field and \( r \) is the distance from that charge to the point of interest. When considering the direction, the electric field vector points away from the charge if it is positive and towards the charge if it is negative.
The exercise involves calculating the electric field components at a certain point in space due to a single point charge, using the principles of Coulomb's Law applied in spherical coordinates.