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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Welcome back Banele — missed you this week. Here are the solutions to your electrostatics questions: QUESTION 1 1.1 Step 1: Explain the purpose of wooden stands. The spheres were placed on wooden stands because wood is an electrical insulator. This prevents charge from flowing from the spheres to the ground, ensuring the spheres retain their charges. 1.2 Step 1: Calculate the total charge. When identical conducting spheres touch, the total charge is shared equally between them. Initial charge on R, Q_R = +8 \, C. Initial charge on S, Q_S = -4 \, C. Total charge Q_total = Q_R + Q_S = +8 \, C + (-4 \, C) = +4 \, C. Step 2: Calculate the charge on each sphere after contact. Since the spheres are identical, the total charge is divided equally. Charge on each sphere after contact, Q' = Q_total2 = (+4 \, C)/(2) = +2 \, C. The net charge on each sphere is +2 \, C after contact and separation. 1.3 Step 1: Describe the electric field pattern. After contact, both spheres R and S have a positive charge of +2 \, C. Electric field lines originate from positive charges and point outwards. Since both spheres are positively charged, the field lines will repel each other in the region between the spheres, creating a region of weaker field or a neutral point directly between them. The field lines will curve away from each other. 1.4 Step 1: Describe the forces on sphere T. Sphere T has a charge of +1 \, C. Sphere R has a charge of +2 \, C. Sphere S has a charge of +2 \, C. • Force on T due to R (F_RT): Since both R and T are positive, the force is repulsive. F_RT acts on T, pushing it away from R (to the right). • Force on T due to S (F_ST): Since both S and T are positive, the force is repulsive. F_ST acts on T, pushing it away from S (to the left). 1.5 Step 1: Convert charges and distances to SI units. Q_R = +2 \, C = 2 × 10^-6 \, C Q_S = +2 \, C = 2 × 10^-6 \, C Q_T = +1 \, C = 1 × 10^-6 \, C r_RT = 10 \, cm = 0.1 \, m r_TS = 20 \, cm = 0.2 \, m Coulomb's constant k = 9 × 10^9 \, N · m^2/C^2. Step 2: Calculate the electrostatic force exerted by R on T (F_RT). Using Coulomb's Law, F = k (|q_1 q_2|)/(r^2): F_RT = (9 × 10^9 \, N · m^2/C^2) |(2 × 10^-6 \, C)(1 × 10^-6 \, C)|(0.1 \, m)^2 F_RT = (9 × 10^9) 2 × 10^-120.01 F_RT = (9 × 10^9) (2 × 10^-10) = 1.8 \, N (to the right) Step 3: Calculate the electrostatic force exerted by S on T (F_ST). F_ST = (9 × 10^9 \, N · m^2/C^2) |(2 × 10^-6 \, C)(1 × 10^-6 \, C)|(0.2 \, m)^2 F_ST = (9 × 10^9) 2 × 10^-120.04 F_ST = (9 × 10^9) (5 × 10^-11) = 0.45 \, N (to the left) Step 4: Calculate the net electrostatic force on T. Let's take the direction to the right as positive. F_net = F_RT + (-F_ST) F_net = 1.8 \, N - 0.45 \, N F_net = 1.35 \, N (to the right) The net electrostatic force experienced by T is 1.35 N to the right. 1.6 Step 1: Define electric field. The electric field at a point is defined as the electrostatic force experienced per unit positive test charge placed at that point. It is a vector quantity. Mathematically, E = (F)/(q). 1.7 Step 1: Calculate the electric field due to R at the location of T (E_R). Using the formula E = k (|Q|)/(r^2): E_R = (9 × 10^9 \, N · m^2/C^2) |2 × 10^-6 \, C|(0.1 \, m)^2 E_R = (9 × 10^9) 2 × 10^-60.01 E_R = (9 × 10^9) (2 × 10^-4) = 1.8 × 10^6 \, N/C (to the right) Step 2: Calculate the electric field due to S at the location of T (E_S). E_S = (9 × 10^9 \, N · m^2/C^2) |2 × 10^-6 \, C|(0.2 \, m)^2 E_S = (9 × 10^9) 2 × 10^-60.04 E_S = (9 × 10^9) (5 × 10^-5) = 0.45 × 10^6 \, N/C (to the left) Step 3: Calculate the magnitude of the net electric field at T. Let's take the direction to the right as positive. E_net = E_R + (-E_S) E_net = (1.8 × 10^6 \, N/C) - (0.45 × 10^6 \, N/C) E_net = 1.35 × 10^6 \, N/C (to the right) The magnitude of the net electric field at the location of T is 1.35 × 10^6 N/C. Drop the next question! 📸