Chapter 25: Q. 32 (page 710)

The electric potential at the dot in FIGURE EX25.32 is $3140 V$ What is charge q?

Short Answer

Expert verified

The value of the potential energy of the dot points is $10 n C$

Step by step solution

Explanation of the the potential energy of (a) point

The equation of the potential energy of a dot point is

$V = \frac{1}{4 π ε_{0}} \frac{q}{r}$

Where q is the charge point, r is the distance and $ε_{0}$

is the permittivity free space.

The value of the distance d from the q point of the figure to A point is

$\begin{array}{rcl} d & = & \sqrt{{(2.0 c m)}^{2} + {(4.0 c m)}^{2}} \\ = & 4.47 c m \end{array}$

$\begin{array}{rcl} r_{1} & = & 2.0 c m \\ = & 0.02 m \\ r_{2} & = & 4.0 c m \\ = & 0.04 m \\ d & = & 4.47 c m \\ = & 0.0447 m \end{array}$

The potential energy at the point A for the responsible charge $q_{1}$

$\begin{array}{rcl} V_{1} & = & \frac{1}{(4 π ε_{0})} \frac{q_{1}}{r_{1}} \\ \frac{1}{(4 π ε_{0})} & = & 9.0 \times 10^{9} N m^{2} / C^{2} \\ q_{1} & = & 5.0 \times 10^{- 9} C \\ r_{1} & = & 0.02 m \\ V_{1} & = & 9.0 \times 10^{9} N m^{2} / C^{2} \times \frac{5.0 \times 10^{- 9} C}{0.02 m} \\ = & 2250 V \end{array}$

The theory of the total energy

The potential energy at the point A for the responsible charge $q_{2}$

$\begin{array}{rcl} V_{2} & = & \frac{1}{(4 π ε_{0})} \frac{q_{2}}{r_{2}} \\ \frac{1}{(4 π ε_{0})} & = & 9.0 \times 10^{9} N m^{2} / C^{2} \\ q_{2} & = & - 5.0 \times 10^{- 9} C \\ r_{2} & = & 0.04 m \\ V_{2} & = & 9.0 \times 10^{9} N m^{2} / C^{2} \frac{(- 5.0 \times 10^{- 9} C)}{0.04 m} \\ = & 1125 V \end{array}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

The electric potential at the dot in FIGURE EX25.32 is $3140 V$ What is charge q?

Short Answer

Step by step solution

Explanation of the the potential energy of (a) point

The theory of the total energy

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Nuclear Physics

Solid State Physics

Famous Physicists

Rotational Dynamics

Force

Work Energy and Power

Study anywhere. Anytime. Across all devices.

The electric potential at the dot in FIGURE EX25.32 is 3140VWhat is charge q?

Short Answer

Step by step solution

Explanation of the the potential energy of (a) point

The theory of the total energy

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Nuclear Physics

Solid State Physics

Famous Physicists

Rotational Dynamics

Force

Work Energy and Power

Study anywhere. Anytime. Across all devices.

The electric potential at the dot in FIGURE EX25.32 is $3140 V$ What is charge q?