   Chapter 15, Problem 69AP

Chapter
Section
Textbook Problem

Each of the electrons in a particle beam has a kinetic energy of 1.60 × 10−17 J. (a) What is the magnitude of the uniform electric field (pointing in the direction of the electrons’ movement) that will stop these electrons in a distance of 10.0 cm? (b) How long will it take to stop the electrons? (c) After the electrons stop, what will they do? Explain.

(a)

To determine
The magnitude of electric field.

Explanation

Given info: The initial kinetic energy of electrons (KE) is 1.6×1017J .

Work done equals the negative of kinetic energy. This is because the final kinetic energy is zero.

Formula to calculate the work done is,

W=FExcosθ

• FE is the electric force.
• x is the displacement.
• θ is the angle between the force and displacement.

The electric force is,

FE=eE

• e is the elementary charge.
• E is the electric field.

Therefore,

eExcosθ=KE

On Re-arranging,

E=KEexcosθ

Substitute 1.6×1017J for KE, 180ο for θ , 10.0 cm for x and 1

(b)

To determine
The required time.

(c)

To determine
The electron’s acceleration.

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