Q. 27 What is the electric potential a... [FREE SOLUTION]

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Chapter 25: Q. 27 (page 710)

What is the electric potential at points A, B, and C in FIGURE EX 25.27?
b. What are the potential differences
螖VAB = VB - VA and
螖VCB = VB - VC?

Short Answer

Expert verified

1. The potential energy at the A, B, C points are 1.80 k.V, 1.80 k.V and 0.90 k.V

2. The potential energy of electrical at the A point is $- 2.8 脳 10^{- 16} J$

Step by step solution

Definition of electrical potential

The value of q in C unit is $2.0 脳 10^{- 19} C$

Transforming the value of r at A point from cm to m is 0.01m

Transforming the value of r at B point from cm to m is 0.01m

Transforming the value of r at C point from cm to m is 0.02m

\begin{array}{rcl} V_{A} & = & \frac{1}{4 蟺 蔚_{0}} \frac{q}{r_{A}} \\ \frac{1}{4 蟺 蔚_{0}} & = & 9.0 脳 10^{9} N . m^{2} / C^{2} \\ q & = & 2.0 脳 10^{- 9} C \\ r_{A} & = & 0.01 m \\ V_{A} & = & 9.0 脳 10^{9} N . m^{2} / C^{2} \frac{2.0 脳 10^{- 9} C}{0.01 m} \\ = & 1.80 k V \\ V_{B} & = & \frac{1}{4 蟺 蔚_{0}} \frac{q}{r_{B}} \\ V_{B} & = & 9.0 脳 10^{9} N . m^{2} / C^{2} \frac{2.0 脳 10^{- 9} C}{0.01 m} \\ = & 1.80 k V \\ V_{C} & = & 9.0 脳 10^{9} N . m^{2} / C^{2} \frac{2.0 脳 10^{- 9} C}{0.02 m} \\ = & 0.90 k V [r_{C} = 0.02 m] \end{array}

Step 2:Definition of the potential energy of electrical at the A point

The formula of the potential energy of electrical is

$\begin{array}{rcl} E_{A} & = & \frac{1}{4 蟺蔚_{0}} \frac{q q_{e}}{r_{A}} \\ \frac{1}{4 蟺蔚_{0}} & = & 9.0 脳 10^{9} N . m^{2} / C^{2} \\ q & = & 2.0 脳 10^{- 9} C \\ r_{A} & = & 0.01 m \\ q_{e} & = & - 1.6 脳 10^{- 19} C \\ E_{A} & = & 9.0 脳 10^{9} N . m^{2} / C^{2} \frac{2.0 脳 10^{- 9} C 脳 - 1.6 脳 10^{- 19} C}{0.01 m} \\ = & - 2.8 脳 10^{- 16} J \\ E_{B} & = & \frac{1}{4 蟺蔚_{0}} \frac{q q_{e}}{r_{B}} = 9.0 脳 10^{9} N . m^{2} / C^{2} \frac{2.0 脳 10^{- 9} C 脳 - 1.6 脳 10^{- 19} C}{0.01 m} \\ = & - 2.8 脳 10^{- 16} J \\ E_{C} & = & 9.0 脳 10^{9} N . m^{2} / C^{2} \frac{2.0 脳 10^{- 9} C 脳 - 1.6 脳 10^{- 19} C}{0.02 m} \\ = & - 1.4 脳 10^{- 16} J [w h e r e r_{c} = 0.02 m] \end{array}$

Hence the potential Difference is;

$\begin{array}{rcl} 鈭� V_{A B} & = & V_{B} - V_{A} \\ = & (1.80 - 1.80) k V \\ = & 0 \end{array}$

and the potential difference of B and C is

$\begin{array}{rcl} 鈭� V_{B C} & = & V_{C} - v_{B} \\ = & (- 0.90 - 1.80) k V \\ = & - 0.90 k V \end{array}$

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91影视

What is the electric potential at points A, B, and C in FIGURE EX 25.27?
b. What are the potential differences
螖VAB = VB - VA and
螖VCB = VB - VC?

Short Answer

Step by step solution

Definition of electrical potential

Step 2:Definition of the potential energy of electrical at the A point

One App. One Place for Learning.

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91影视

What is the electric potential at points A, B, and C in FIGURE EX 25.27?b. What are the potential differences螖VAB = VB - VA and螖VCB = VB - VC?

Short Answer

Step by step solution

Definition of electrical potential

Step 2:Definition of the potential energy of electrical at the A point

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Nuclear Physics

Conservation of Energy and Momentum

Thermodynamics

Electrostatics

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

What is the electric potential at points A, B, and C in FIGURE EX 25.27?
b. What are the potential differences
螖VAB = VB - VA and
螖VCB = VB - VC?