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.
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Step 1: Describe the electric field pattern (Part a) Sphere A is positively charged (+5.0 Nc), and sphere B is negatively charged (-4.0 Nc). Electric field lines originate from positive charges and terminate on negative charges. • The electric field lines start from sphere A and end on sphere B, curving between them. • The lines are perpendicular to the surface of both spheres. • The density of the field lines is highest in the region between the spheres, indicating a stronger electric field there. • Since the magnitude of charge on A (+5.0 Nc) is greater than on B (-4.0 Nc), some field lines will originate from A and extend outwards into space, not terminating on B. Step 2: Determine the magnitude of the electric force (Part b) The magnitude of the electric force between two point charges is given by Coulomb's Law: F = k (|q_A q_B|)/(r^2) where k = 8.99 × 10^9 N m^2/C^2 is Coulomb's constant, q_A and q_B are the magnitudes of the charges, and r is the distance between them. Given: q_A = +5.0 Nc = +5.0 × 10^-9 C q_B = -4.0 Nc = -4.0 × 10^-9 C r = 3.5 cm = 0.035 m Substitute the values into Coulomb's Law: F &= (8.99 × 10^9 N m^2/C^2) |(5.0 × 10^-9 C)(-4.0 × 10^-9 C)|(0.035 m)^2 \\ &= (8.99 × 10^9) 20.0 × 10^-18(0.035)^2 N \\ &= (8.99 × 10^9) 2.0 × 10^-170.001225 N \\ &= 1.798 × 10^-70.001225 N \\ &≈ 1.4677 × 10^-4 N The magnitude of the electric force is 1.47 × 10^-4 N. Step 3: Calculate the value of angle (Part c) Sphere A is in equilibrium under the influence of three forces: 1. Gravitational force (weight) W = mg, acting vertically downwards. 2. Electric force F_e, acting horizontally towards sphere B (attraction). 3. Tension T in the string, acting along the string at an angle to the vertical. For equilibrium, the net force in both horizontal and vertical directions must be zero. Given: Mass of sphere A, m = 4.5 × 10 kg = 45 kg Acceleration due to gravity, g = 9.81 m/s^2 Electric force, F_e = 1.4677 × 10^-4 N (from Part b) First, calculate the weight of sphere A: W = mg = (45 kg)(9.81 m/s^2) = 441.45 N Resolve the tension T into its components: • Vertical component: T • Horizontal component: T Equilibrium equations: • Vertical forces: T = W = 441.45 N • Horizontal forces: T = F_e = 1.4677 × 10^-4 N Divide the horizontal equation by the vertical equation: (T )/(T ) = (F_e)/(W) = (F_e)/(W) Substitute the values: = 1.4677 × 10^-4 N441.45 N ≈ 3.3248 × 10^-7 Now, calculate : = (3.3248 × 10^-7) ≈ 1.905 × 10^-5 degrees The value of the angle is 1.91 × 10^-5 degrees. Send me the next one 📸