### 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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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

### Problem Statement

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?

### Explanation

In 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 (\( V_{\infty} \)): 0V

Using 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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