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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4.1 Electrons were removed from sphere X. A positive charge indicates a deficit of electrons, meaning electrons were taken away from the sphere. 4.2 The electric field at a point is defined as the electrostatic force per unit positive test charge experienced at that point. 4.3 The magnitude of the electric field due to the charged sphere X is greater at point A. The electric field strength (E) is inversely proportional to the square of the distance (r) from the charge (E (1)/(r^2)). Since point A is closer to sphere X (10 mm) than point B (30 mm), the electric field is stronger at A. 4.4 Here is a description of the labelled vector diagram: • Draw sphere X at the center. • Draw point Z to the left of X, 10 mm away. • Draw point Y to the right of X, 30 mm away. • Sphere X has a positive charge (+1.5 × 10^-16 C). • Point charge Z has a positive charge (+3.2 × 10^-16 C). Since X and Z are both positive, they repel. The force exerted by Z on X (F_XZ) will be directed away from Z, which is to the right. • Point charge Y has a negative charge (-2.8 × 10^-16 C). Since X is positive and Y is negative, they attract. The force exerted by Y on X (F_XY) will be directed towards Y, which is to the right. • Therefore, both force vectors (F_XZ and F_XY) originate from X and point to the right. 4.5 Step 1: Identify the given values and convert units. Charge of sphere X, Q_X = +1.5 × 10^-16 C Charge of point Z, Q_Z = +3.2 × 10^-16 C Charge of point Y, Q_Y = -2.8 × 10^-16 C Distance between X and Z, r_XZ = 10 mm = 0.010 m Distance between X and Y, r_XY = 30 mm = 0.030 m Coulomb's constant, k = 8.99 × 10^9 N·m^2/C^2 Step 2: Calculate the electrostatic force on X due to Z (F_XZ). Since both charges are positive, the force is repulsive, directed to the right. F_XZ = (k|Q_X Q_Z|)/(r_XZ)^2 F_XZ = (8.99 × 10^9 N·m^2/C^2)(1.5 × 10^-16 C)(3.2 × 10^-16 C)(0.010 m)^2 F_XZ = (8.99 × 10^9)(4.8 × 10^-32)1.0 × 10^-4 N F_XZ = 4.3152 × 10^-18 N (to the right) Step 3: Calculate the electrostatic force on X due to Y (F_XY). Since X is positive and Y is negative, the force is attractive, directed to the right. F_XY = (k|Q_X Q_Y|)/(r_XY)^2 F_XY = (8.99 × 10^9 N·m^2/C^2)(1.5 × 10^-16 C)(2.8 × 10^-16 C)(0.030 m)^2 F_XY = (8.99 × 10^9)(4.2 × 10^-32)9.0 × 10^-4 N F_XY = 4.1953 × 10^-19 N (to the right) Step 4: Calculate the net electrostatic force on sphere X. Since both forces are in the same direction (to the right), we add their magnitudes. F_net = F_XZ + F_XY F_net = (4.3152 × 10^-18 N) + (4.1953 × 10^-19 N) F_net = (4.3152 × 10^-18 N) + (0.41953 × 10^-18 N) F_net = (4.3152 + 0.41953) × 10^-18 N F_net = 4.73473 × 10^-18 N The net electrostatic force on sphere X is 4.73 × 10^-18 N to the right. Send me the next one 📸