### Problem StatementA spherical drop of water carrying a charge of 10.0 pC has a potential of 200.0 V at its surface (with \( V = 0 \) at infinity). What is the radius of the drop?### ExplanationIn this problem, we are given a spherical drop of water with a known charge and electric potential at its surface. We are asked to determine the radius of this spherical drop.Let's denote the given information as follows:- Charge (\( Q \)) of the water drop: 10.0 picoCoulombs (pC) = \( 10.0 \times 10^{-12} \) Coulombs (C)- Electric potential (\( V \)) at the surface: 200.0 Volts (V)- Potential at infinity (\( V_{\infty} \)): 0VUsing the formula for the electric potential on the surface of a sphere, which is given by:\[ V = \frac{1}{4 \pi \epsilon_0} \frac{Q}{r} \]where:- \( \epsilon_0 \) is the permittivity of free space (\( 8.854 \times 10^{-12} \, \text{F/m} \))- \( r \) is the radius of the sphere.Rearranging the formula to solve for \( r \):\[ r = \frac{1}{4 \pi \epsilon_0} \frac{Q}{V} \]Now, substituting the given values into the formula:\[ r = \frac{1}{4 \pi \times 8.854 \times 10^{-12}} \frac{10.0 \times 10^{-12}}{200.0} \]Evaluate the expression to find the radius \( r \). **Instructions for Solving Physics Problems: A Step-by-Step Approach**---**Please follow these instructions:****I) Identify the physics quantities and visualize the situation**1. **Given quantities:** - List the quantities provided in the problem statement.2. **Unknown quantities:** - Identify which quantities need to be found.3. **Sketch the situation given in the problem:** - Create a visual representation of the scenario to better understand the physical situation.---**II) Identify the physics principles involved and the corresponding generic steps**4. **Principle(s)/ Key idea(s):** - Determine the fundamental physics principles that apply to the problem.5. **Equations:** - List the relevant equations that arise from the identified principles.6. **Analytic solution (20%):** - Solve the equations analytically to derive the solution in a general form.7. **Numeric solution:** - Substitute the given quantities into the analytic solution to calculate the numeric answer.8. **Final Answer:** - Present the final answer clearly, ensuring all conditions are met.---**IV) Self check**9. **Unit check:** - Verify that the units of the final answer are consistent and appropriate for the quantity being calculated.10. **Number check:** - Review the calculations to ensure numerical accuracy.---By following these steps, you can systematically approach and solve physics problems accurately and efficiently.

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Answered: A spherical drop of water carrying a…

A spherical drop of water carrying a charge of 10.0 pC has a potential of 200.0 V at its surface (with V=0 at infinity). What is the radius of the drop?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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