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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
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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**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.
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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