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Question 2 Consider Two Charges, Where One (+3.80nC) Is at the Origin and the Other (-14.4nC) Is at the Position X=2.86 86 Cm. Find the

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Question 2 Consider two charges, where one (+3.80nC) is at the origin and the other (-14.4nC) is at the position x=2.86 86 cm. Find the xcoordinate where a proton would experience zero net force. Answer: square

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Answer

Here's how to find the x-coordinate where a proton would experience zero net force:**1. Understand the Problem**A proton placed between two charges of opposite signs will experience two forces in opposite directions. We need to find the point where these forces balance each other out.**2. Coulomb's Law**The force between two charges is given by Coulomb's Law:F = k * |q1 * q2| / r^2Where:* F is the force* k is Coulomb's constant (8.99 x 10^9 N m^2/C^2)* q1 and q2 are the charges* r is the distance between the charges**3. Set up the Equation**Let x be the distance from the origin where the proton experiences zero net force. The distance from the positive charge (+3.80 nC) to the proton is x. The distance from the negative charge (-14.4 nC) to the proton is (2.86 cm - x), or (0.0286 m - x).The force from the positive charge on the proton (q_p) is:F1 = k * |q1 * q_p| / x^2The force from the negative charge on the proton is:F2 = k * |q2 * q_p| / (0.0286 - x)^2Since the net force is zero, F1 = F2:k * |q1 * q_p| / x^2 = k * |q2 * q_p| / (0.0286 - x)^2**4. Simplify and Solve**Notice that k and q_p cancel out:|q1| / x^2 = |q2| / (0.0286 - x)^2Substitute the values of q1 and q2:3.80 x 10^-9 / x^2 = 14.4 x 10^-9 / (0.0286 - x)^2Simplify further:3.80 / x^2 = 14.4 / (0.0286 - x)^2Cross-multiply:3.80 * (0.0286 - x)^2 = 14.4 * x^2Take the square root of both sides:√(3.80/14.4) * (0.0286-x) = x0.515 * (0.0286 - x) = x0.0147 - 0.515x = x0.0147 = 1.515xx ≈ 0.0097 m**5. Convert to cm**x ≈ 0.0097 m * 100 cm/m = 0.97 cm**Answer:** 0.97 cm (approximately)