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
Let's go through the solution you provided for the net force on q_1. First, let's recall the charges and distances from the previous context: q_1 = +1.0 nC = +1.0 × 10^-9 C q_2 = -3.0 nC = -3.0 × 10^-9 C q_3 = +5.0 nC = +5.0 × 10^-9 C Distance between q_1 and q_3 is 2.0 cm = 0.02 m. Distance between q_2 and q_3 is 4.0 cm = 0.04 m. The solution you provided makes a reasonable assumption about the arrangement of the charges, which was not explicitly stated in the original problem. It assumes a linear arrangement where q_1 and q_2 are on opposite sides of q_3. This means the distance between q_1 and q_2 is the sum of their distances from q_3: 2.0 cm + 4.0 cm = 6.0 cm = 0.06 m. Let's verify the steps: Step 1: Calculate the force of q_3 on q_1 (F_1). The formula for Coulomb's Law is F = k (|q_a||q_b|)/(r^2), where k = (1)/(4_0) = 9 × 10^9 N·m^2/C^2. F_1 = (1)/(4_0) (|q_1||q_3|)/(r_1^2) F_1 = (9 × 10^9 N·m^2/C^2) × (1.0 × 10^-9 C)(5.0 × 10^-9 C)(0.02 m)^2 F_1 = 9 × 10^9 × 5.0 × 10^-180.0004 N F_1 = 9 × 10^9 × 1.25 × 10^-14 N F_1 = 112.5 × 10^-6 N Since q_1 and q_3 are both positive, the force is repulsive. The value 112 × 10^-6 N is a correctly rounded value. Step 2: Calculate the force of q_2 on q_1 (F_2). The distance between q_1 and q_2 is r_2 = 0.06 m. F_2 = (1)/(4_0) (|q_2||q_1|)/(r_2^2) F_2 = (9 × 10^9 N·m^2/C^2) × (3.0 × 10^-9 C)(1.0 × 10^-9 C)(0.06 m)^2 F_2 = 9 × 10^9 × 3.0 × 10^-180.0036 N F_2 = 9 × 10^9 × 8.333... × 10^-16 N F_2 = 7.5 × 10^-6 N Since q_1 is positive and q_2 is negative, the force is attractive. This calculation is correct. Step 3: Determine the net force on q_1. Given the assumed linear arrangement (e.g., q_2 - q_3 - q_1), the force F_1 (repulsive from q_3) acts away from q_3, and the force F_2 (attractive from q_2) acts towards q_2. These two forces are in opposite directions. Therefore, the net force is the difference between their magnitudes. F_R = F_1 - F_2 F_R = 112.5 × 10^-6 N - 7.5 × 10^-6 N F_R = (112.5 - 7.5) × 10^-6 N F_R = 105 × 10^-6 N The value 104.5 × 10^-6 N in your provided solution is slightly different due to rounding F_1 to 112 × 10^-6 N before subtraction. If we use 112 × 10^-6 N, then 112 × 10^-6 N - 7.5 × 10^-6 N = 104.5 × 10^-6 N. This is consistent with the rounding in the provided solution. The solution you provided is ✅ Correct based on the implied linear arrangement of charges where q_1 and q_2 are on opposite sides of q_3. The net force on q_1 is 104.5 × 10^-6 N. That's 2 down. 3 left today — send the next one.