Electric Field Due to Multiple Charges?

📌 CONCEPT: The electric field due to multiple charges is the vector sum of the electric fields due to each charge at a given point in space.

📐 RULE / FORMULA: To calculate the total electric field, we use the principle of superposition, which states that the electric field at a point due to multiple charges is the vector sum of the electric fields due to each charge. The electric field due to a point charge is given by E = k · q / r^2, where k is Coulomb's constant, q is the charge, and r is the distance between the charge and the point.

💡 WORKED EXAMPLE: Let's consider the given problem. First, we calculate the electric field due to the +4μC charge at point P. Using the formula E1 = k · q1 / r1^2, we get E1 = (9 × 10^9) · (4 µ C) / (0.3 m)^2 = 4.8 × 10^9 N/C. Next, we calculate the electric field due to the -2μC charge at point P. Using the formula E2 = k · q2 / r2^2, we get E2 = (9 × 10^9) · (-2 µ C) / (0.2 m)^2 = -9 × 10^9 N/C. Finally, we find the total electric field at point P by adding E1 and E2.

⚠️ COMMON MISTAKE: Students often forget to consider the direction of the electric field due to each charge and may make errors when adding the fields vectorially.