This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here's how to calculate the resultant electrostatic force on Q2. Given: Q_1 = +3 × 10^-6 C Q_2 = -4 × 10^-6 C Q_3 = +6 × 10^-6 C r_12 = 15 cm = 0.15 m r_23 = 25 cm = 0.25 m Coulomb's constant k = 8.99 × 10^9 N·m^2/C^2 Step 1: Calculate the electrostatic force exerted by Q_1 on Q_2 (F_12). Since Q_1 is positive and Q_2 is negative, they will attract each other. The force F_12 on Q_2 will be directed towards Q_1 (to the left). Using Coulomb's Law: F_12 = k (|Q_1 Q_2|)/(r_12)^2 F_12 = (8.99 × 10^9 N·m^2/C^2) |(3 × 10^-6 C)(-4 × 10^-6 C)|(0.15 m)^2 F_12 = (8.99 × 10^9) 12 × 10^-120.0225 F_12 = 4.7946 N The force F_12 is 4.7946 N to the left. Step 2: Calculate the electrostatic force exerted by Q_3 on Q_2 (F_32). Since Q_3 is positive and Q_2 is negative, they will attract each other. The force F_32 on Q_2 will be directed towards Q_3 (to the right). Using Coulomb's Law: F_32 = k (|Q_3 Q_2|)/(r_23)^2 F_32 = (8.99 × 10^9 N·m^2/C^2) |(6 × 10^-6 C)(-4 × 10^-6 C)|(0.25 m)^2 F_32 = (8.99 × 10^9) 24 × 10^-120.0625 F_32 = 3.45216 N The force F_32 is 3.45216 N to the right. Step 3: Calculate the resultant electrostatic force on Q_2. The forces F_12 and F_32 act in opposite directions on Q_2. Let's define the direction to the right as positive. F_net = F_32 - F_12 F_net = 3.45216 N - 4.7946 N F_net = -1.34244 N The negative sign indicates that the resultant force is directed to the left. The magnitude of the resultant force is 1.34 N (rounded to two decimal places). The direction of the resultant force is towards Q_1 (to the left). The resultant electrostatic force acting on Q_2 is 1.34 N to the left. Last free one today — make it count tomorrow, or type /upgrade for unlimited.