Chapter 26: Q.15 (page 738)

The electric potential along the x-axis is $V = 100 e^{- 2 x} V$ , where $x$ is in meters. What is $E_{x}$ at (a)role="math" localid="1649581712352" $x = 1.0 m$ and (b) role="math" localid="1649581719374" $x = 2.0 m$ ?

Short Answer

Expert verified

$(a) E_{x} = 27 V / m (b) E_{x} = 3.7 V / m$

Step by step solution

Given information and theory used

Given : The electric potential along the x-axis is : $V = 100 e^{- 2 x} V$

(a) $x = 1 . 0 m$ and (b) $x = 2.0 m$

Theory used :

The electric field is expressed as a function of potential as :

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

Calculating Ex

The negative derivative of the potential $V = 100 e^{- 2 x} V$ is equivalent to the component of the electric field. As a result,

role="math" localid="1649581602113" $E (x) = - \frac{d V (x)}{d x} = - 100 (- 2 e^{- 2 x}) V / m = 200 e^{- 2 x} V / m$

(a) We have $E_{x} = 27 V / m at a = 1.0 m$ .

(a) We have $E_{x} = 3.7 V / m at x = 2.0 m$ .

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The electric potential along the x-axis is $V = 100 e^{- 2 x} V$ , where $x$ is in meters. What is $E_{x}$ at (a)role="math" localid="1649581712352" $x = 1.0 m$ and (b) role="math" localid="1649581719374" $x = 2.0 m$ ?

Short Answer

Step by step solution

Given information and theory used

Calculating Ex

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The electric potential along the x-axis is V=100e-2xV, wherex is in meters. What is Ex at (a)role="math" localid="1649581712352" x=1.0m and (b) role="math" localid="1649581719374" x=2.0m?

Short Answer

Step by step solution

Given information and theory used

Calculating Ex

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electrostatics

Energy Physics

Fields in Physics

Particle Model of Matter

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Space Physics

Study anywhere. Anytime. Across all devices.

The electric potential along the x-axis is $V = 100 e^{- 2 x} V$ , where $x$ is in meters. What is $E_{x}$ at (a)role="math" localid="1649581712352" $x = 1.0 m$ and (b) role="math" localid="1649581719374" $x = 2.0 m$ ?