A spherical drop of water carrying a charge of 31 pC has a potential of 380 V at its surface (with V= 0 at infinity). (a) What is the radius of the drop? (b) If two such drops of the same charge and radius combine to form a single spherical drop, what is the potential at the surface of the new drop? (a) Number i Units (b) Number i Units
A spherical drop of water carrying a charge of 31 pC has a potential of 380 V at its surface (with V= 0 at infinity). (a) What is the radius of the drop? (b) If two such drops of the same charge and radius combine to form a single spherical drop, what is the potential at the surface of the new drop? (a) Number i Units (b) Number i Units
College Physics
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Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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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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![**Physics Problem Example**
A spherical drop of water carrying a charge of \(31 \text{ pC}\) has a potential of \(380 \text{ V}\) at its surface (with \(V = 0\) at infinity).
1. **Question (a):** What is the radius of the drop?
2. **Question (b):** If two such drops of the same charge and radius combine to form a single spherical drop, what is the potential at the surface of the new drop?
**Solve the following problems:**
**(a)**
- **Number:** [Enter your answer]
- **Units:** [Select the units]
**(b)**
- **Number:** [Enter your answer]
- **Units:** [Select the units]
---
**Explanation:**
To solve question **(a)**, you can use the formula for the potential of a spherical drop:
\[ V = \frac{kQ}{R} \]
Where:
- \( V \) is the potential (\(380 \text{ V}\)),
- \( k \) is Coulomb's constant (\(8.99 \times 10^9 \text{ N m}^2/\text{C}^2\)),
- \( Q \) is the charge (\(31 \text{ pC} = 31 \times 10^{-12} \text{ C}\)),
- \( R \) is the radius of the drop.
Rearrange to solve for \( R \):
\[ R = \frac{kQ}{V} \]
For question **(b)**, consider the conservation of charge and volume for the combination of two spherical drops.
---
**Textbook and Media:**
For further reading, refer to your physics textbook, section ‘Electrostatics and Capacitors,’ or watch related eTextbook and Media resources for a step-by-step guide and detailed explanations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba35cc5f-959d-4f80-acdd-e9cc0bd31dfa%2F2a79e195-b3a5-4df3-810e-6be47c4f7ed0%2Fnjheec_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Physics Problem Example**
A spherical drop of water carrying a charge of \(31 \text{ pC}\) has a potential of \(380 \text{ V}\) at its surface (with \(V = 0\) at infinity).
1. **Question (a):** What is the radius of the drop?
2. **Question (b):** If two such drops of the same charge and radius combine to form a single spherical drop, what is the potential at the surface of the new drop?
**Solve the following problems:**
**(a)**
- **Number:** [Enter your answer]
- **Units:** [Select the units]
**(b)**
- **Number:** [Enter your answer]
- **Units:** [Select the units]
---
**Explanation:**
To solve question **(a)**, you can use the formula for the potential of a spherical drop:
\[ V = \frac{kQ}{R} \]
Where:
- \( V \) is the potential (\(380 \text{ V}\)),
- \( k \) is Coulomb's constant (\(8.99 \times 10^9 \text{ N m}^2/\text{C}^2\)),
- \( Q \) is the charge (\(31 \text{ pC} = 31 \times 10^{-12} \text{ C}\)),
- \( R \) is the radius of the drop.
Rearrange to solve for \( R \):
\[ R = \frac{kQ}{V} \]
For question **(b)**, consider the conservation of charge and volume for the combination of two spherical drops.
---
**Textbook and Media:**
For further reading, refer to your physics textbook, section ‘Electrostatics and Capacitors,’ or watch related eTextbook and Media resources for a step-by-step guide and detailed explanations.
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