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
Step 1: Identify the given values for Question 5. The charges on the spheres are q_1 = 2 × 10^-7 C and q_2 = 3 × 10^-7 C. The distance between the spheres is r = 30 cm = 0.30 m. The electrostatic constant for air is k = (1)/(4_0) = 9 × 10^9 N m^2/C^2. Step 2: Calculate the electrostatic force using Coulomb's Law. The formula for Coulomb's Law is F = k (q_1 q_2)/(r^2). F = (9 × 10^9 N m^2/C^2) (2 × 10^-7 C) × (3 × 10^-7 C)(0.30 m)^2 F = (9 × 10^9) 6 × 10^-140.09 N F = (9 × 10^9) × (66.66... × 10^-14) N F = 600 × 10^-5 N F = 6 × 10^-3 N Since both charges are positive, the force is repulsive. The force is 6 × 10^-3 N and is repulsive. Step 3: Identify the given values for Question 6 (a). The charge on the first sphere is q_1 = 0.4 = 0.4 × 10^-6 C. The force experienced is F = 0.2 N. The charge on the second sphere is q_2 = 0.8 = 0.8 × 10^-6 C. The electrostatic constant for air is k = 9 × 10^9 N m^2/C^2. Step 4: Calculate the distance between the spheres for Question 6 (a). Using Coulomb's Law, F = k (q_1 q_2)/(r^2). We need to find r. Rearranging the formula for r^2: r^2 = k (q_1 q_2)/(F) Substitute the given values: r^2 = (9 × 10^9 N m^2/C^2) (0.4 × 10^-6 C) × (0.8 × 10^-6 C)0.2 N r^2 = (9 × 10^9) 0.32 × 10^-120.2 m^2 r^2 = (9 × 10^9) × (1.6 × 10^-12) m^2 r^2 = 14.4 × 10^-3 m^2 r^2 = 0.0144 m^2 Now, take the square root to find r: r = sqrt(0.0144 m)^2 r = 0.12 m Converting to centimeters: r = 0.12 × 100 cm = 12 cm The distance between the spheres is 0.12 m or 12 cm. Step 5: Determine the force on the second sphere due to the first for Question 6 (b). According to Newton's third law, the force exerted by the first sphere on the second sphere is equal in magnitude and opposite in direction to the force exerted by the second sphere on the first sphere. Therefore, if the first sphere experiences a force of 0.2 N due to the second sphere, the second sphere will also experience a force of 0.2 N due to the first sphere. The force on the second sphere due to the first sphere is 0.2 N. That's 2 down. 3 left today — send the next one.