3. Three point charges are placed at the following points on the x-axis: +2.0mu Calx=0 at x=40.0 cm, and -5.0mu C at x=120.0 cm. Determine the force on the -3.0mu C charge. Iiil [ans: 0.55 N toward the negative x-direction or 0.55 N [left]]

Here's how to determine the force on the -3.0 μC charge:<br /><br />**1. Define Variables and Constants:**<br /><br />* q₁ = +2.0 μC = +2.0 x 10⁻⁶ C (charge at x = 0)<br />* q₂ = -3.0 μC = -3.0 x 10⁻⁶ C (charge at x = 40.0 cm = 0.40 m)<br />* q₃ = -5.0 μC = -5.0 x 10⁻⁶ C (charge at x = 120.0 cm = 1.20 m)<br />* k = 8.99 x 10⁹ Nm²/C² (Coulomb's constant)<br />* r₁₂ = 0.40 m (distance between q₁ and q₂)<br />* r₂₃ = 1.20 m - 0.40 m = 0.80 m (distance between q₂ and q₃)<br /><br />**2. Calculate the Force between q₁ and q₂ (F₁₂):**<br /><br />The force F₁₂ is attractive since the charges have opposite signs. Its direction is along the positive x-axis (to the right).<br /><br />F₁₂ = (k * |q₁| * |q₂|) / r₁₂²<br />F₁₂ = (8.99 x 10⁹ Nm²/C² * 2.0 x 10⁻⁶ C * 3.0 x 10⁻⁶ C) / (0.40 m)²<br />F₁₂ = 0.337 N (to the right)<br /><br />**3. Calculate the Force between q₂ and q₃ (F₂₃):**<br /><br />The force F₂₃ is repulsive since the charges have the same signs. Its direction is along the negative x-axis (to the left).<br /><br />F₂₃ = (k * |q₂| * |q₃|) / r₂₃²<br />F₂₃ = (8.99 x 10⁹ Nm²/C² * 3.0 x 10⁻⁶ C * 5.0 x 10⁻⁶ C) / (0.80 m)²<br />F₂₃ = 0.212 N (to the left)<br /><br />**4. Calculate the Net Force on q₂:**<br /><br />The net force on q₂ is the vector sum of F₁₂ and F₂₃. Since they act along the x-axis, we can simply subtract their magnitudes, considering their directions:<br /><br />F_net = F₂₃ - F₁₂ (Since F₂₃ is to the left and F₁₂ is to the right)<br />F_net = 0.212 N - 0.337 N<br />F_net = -0.125 N<br /><br />**5. Interpret the Result:**<br /><br />The negative sign indicates that the net force on the -3.0 μC charge is directed towards the negative x-direction (to the left) with a magnitude of 0.125 N.<br /><br />**Important Note:** The provided answer (0.55 N) is incorrect based on the given charges and distances. The correct answer, following the principles of Coulomb's Law, is 0.125 N to the left. Double-check the problem statement to ensure all values are correctly transcribed.<br />