91Ó°ÊÓ

Coulomb's Law is the cornerstone of understanding electric forces between charged objects. It states that the electric force (\( F \)) between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Mathematically, it is expressed as:

\[F = \frac{K \cdot |q_1 \cdot q_2|}{r^2}\]where \( K = 8.99 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2 \) is Coulomb’s constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the distance between them.

This law helps explain how charged rods can exert forces on each other and on other charges nearby. By calculating the electric fields they create, we can further explore how these forces manifest.

The electric force is crucial in determining how charged particles interact with each other. It acts through the electric fields generated by charges and influences any nearby charged objects.

For an electron placed at point \( P \), the force it experiences can be determined using the formula:

• Formula: \( F = qE \)
• Where: \( q \) is the charge of the electron (\( -1.6 \times 10^{-19} \, \text{C} \)) and \( E \) is the electric field at point \( P \).

Considering the direction, since an electron has a negative charge, the force is directed opposite to the electric field. Understanding this interaction makes it easier to predict the behavior of charged particles under various conditions.

Charged rods, when aligned perpendicularly, create unique electric fields at specific points around them. Each rod has a uniform charge distribution along its length, affecting how the field behaves:

• Positive Rod: Generates an electric field that points away from the rod.
• Negative Rod: Creates a field pointing towards itself.

At point \( P \), which is equidistant from both rods, these fields interact. Calculating the electric field from each rod involves considering its charge (\( q = \pm 2.5 \, \mu\text{C} \)) and the distance from \( P \), providing insights into their combined effect.

The direction of an electric field is determined by the charge distribution and orientation of the sources. For our rods:

• The positive rod's field points radially outward.
• The negative rod's field points inward.

At point \( P \), these directions are perpendicular due to the rods' placement at right angles. The resultant electric field's magnitude can be found using the Pythagorean theorem:

\[E_{\text{net}} = \sqrt{E_1^2 + E_2^2}\]To find the net direction, we use the tangent function, where the two component fields form the sides of a right triangle, providing a clear picture of how they combine at \( P \).