Chapter 23: Q22 P (page 988)

An electric field of $1 \times 10^{6} N / C$ acts on an electron, resulting in an acceleration of $1.8 \times 10^{17} m / s^{2}$ for a short time. What is the magnitude of the radiative electric field observed at a location a distance of $2 cm$ away along a line perpendicular to the direction of the acceleration?

Short Answer

Expert verified

The radiative electric field is $1.44 \times 10^{- 7} N / C$ .

Step by step solution

Given data

Applied electric field:

$E = 1 \times 10^{6} N / C$

Acceleration of the electron:

$a = 1.8 \times 10^{17} m / s^{2}$

Distance of measurement of radiative electric field

$r = 2 cm = 2 \cdot (1 cm \times \frac{1 m}{100 cm}) = 0.02 m$

Determine the concept of electric field

The radiative electric field of a particle of charge and acceleration is:

$E = \frac{1}{4 π ε_{0}} \frac{q a}{c^{2} r}$ ……. (i)

Here, $ε_{0}$ is the permittivity of free space with value $\frac{1}{4 π ε_{0}} = 9 \times 10^{9} N . m^{2} / C^{2}$

Here, $E$ is the speed of light in vacuum with charge $c = 3 \times 10^{8} m / s$ .

Determine the radiative electric field

From equation (i), the radiative electric field for the electron with charge $1.6 \times 10^{- 19} C$ is calculated as:

$E = 9 \times 10^{9} N . m^{2} / C^{2} \times \frac{1.6 \times 10^{- 19} C \times 1.8 \times 10^{17} m / s^{2}}{{(3 \times 10^{8} m / s)}^{2} \times 0.02 m} = 1.44 \times 10^{- 7} N / C$

Thus, the field is $1.44 \times 10^{- 7} N / C$ .

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Short Answer

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Determine the concept of electric field

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An electric field of 1×106N/C acts on an electron, resulting in an acceleration of 1.8×1017m/s2 for a short time. What is the magnitude of the radiative electric field observed at a location a distance of 2cm away along a line perpendicular to the direction of the acceleration?

Short Answer

Step by step solution

Given data

Determine the concept of electric field

Determine the radiative electric field

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Medical Physics

Fields in Physics

Nuclear Physics

Atoms and Radioactivity

Electrostatics

Study anywhere. Anytime. Across all devices.