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 $q_{2}$

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

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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

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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

Circular Motion and Gravitation

Rotational Dynamics

Electricity

Mechanics and Materials

Solid State Physics

Famous Physicists

Study anywhere. Anytime. Across all devices.

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