Chapter 26: Q. 9 (page 737)

Figure EX26.9shows a graph of $V versus x$ in a region of space. The potential is independent of y and z. What is $E_{x}$ at
(a) $x = - 2 c m$ , (b) $x = 0 c m$ , and (c) $x = 2 c m$ ?

Short Answer

Expert verified

a. $E_{x = - 2} = 5 V / m$

b. $E_{x = 0 c m} = - 10 V / m$

c. $E_{x = 2 c m} = 5 V / m$

Step by step solution

Given information and formula used

Given graph :

Positions : (a) $x = - 2 c m$ , (b) $x = 0 c m$ , and (c) $x = 2 c m$

Theory used :

The electric field strength is assumed to be independent of both $y and z$ positions, i.e., it only depends on $x$ position. As a result,

$E = - \frac{d V}{d x}$

Calculating Ex at (a) x = -2 cm, (b) x = 0 cm, and (c) x = 2 cm

Finding the derivative of the potential at the stated points of interest, we have :

a. At a distance of $x = - 2 c m$ , the electric field strength will be :

$E_{x = - 2 c m} = - \frac{d}{d x} V_{x = - 2 c m} = - \frac{- 10 - 0}{- 1 - (- 3)} = 5 V / m$

b. At position $x = 0 c m$ , the electric field strength will be

$E_{x = 0 c m} = - \frac{d}{d x} V_{x = 0 c m} = - \frac{10 - (- 10)}{1 - (- 1)} = - 10 V / m$

c. At location $x = 2 c m$ , the electric field strength will be

$E_{x = 2 c m} = - \frac{d}{d x} V_{x = 2 c m} = - \frac{0 - 10}{3 - 1} = 5 V / m$

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Figure EX26.9shows a graph of $V versus x$ in a region of space. The potential is independent of y and z. What is $E_{x}$ at
(a) $x = - 2 c m$ , (b) $x = 0 c m$ , and (c) $x = 2 c m$ ?

Short Answer

Step by step solution

Given information and formula used

Calculating Ex at (a) x = -2 cm, (b) x = 0 cm, and (c) x = 2 cm

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Figure EX26.9shows a graph of Vversusxin a region of space. The potential is independent of y and z. What is Exat (a) x=-2cm, (b) x=0cm, and (c) x=2cm?

Short Answer

Step by step solution

Given information and formula used

Calculating Ex at (a) x = -2 cm, (b) x = 0 cm, and (c) x = 2 cm

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Classical Mechanics

Conservation of Energy and Momentum

Work Energy and Power

Electricity

Radiation

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

Figure EX26.9shows a graph of $V versus x$ in a region of space. The potential is independent of y and z. What is $E_{x}$ at
(a) $x = - 2 c m$ , (b) $x = 0 c m$ , and (c) $x = 2 c m$ ?