Chapter 23: Q. 30 (page 654)

An electron in a vacuum chamber is fired with a speed of $8300 k m / s$ toward a large, uniformly charged plate $75 c m$ away. The electron reaches a closest distance of $15 c m$ before being repelled. What is the plate’s surface charge density?

Short Answer

Expert verified

The plate’s surface charge density is $2.8 x 10^{- 9} C / m ²$

Step by step solution

Given information and formula used

Given :

The electron is fired with a speed of : $8300 k m / s$

Distance from the uniformly charged plate : $75 c m$

The electron reaches a closest distance of : $15 c m$

Theory used :

The electric field owing to an infinite plane is calculated as follows:

$E = \frac{σ}{2 ε_{0}}$

The electron's force

$F = e E = \frac{e σ}{ε_{0}}$

The electron's work consists of the following:

$W = F d = \frac{d e σ}{ε_{0}} d = \frac{1}{2} m v^{2} \Rightarrow \frac{d e σ}{ε_{0}} = \frac{1}{2} m v^{2}$

Calculating the plate’s surface charge density

Finding $d$ :

$d = d ₁ - d ₂ = 75 c m - 15 c m = 60 c m = 0.6 m$

Finally, we locate $a$ :

\frac{d e σ}{ε_{0}} = \frac{1}{2} m v^{2} \Rightarrow σ = \frac{m v^{2} ε_{0}}{2 d e} = \frac{(9.11 \times 10^{- 31}) \times (8.3 \times 10^{6}) ² \times (8.85 \times 10^{- 12})}{2 x 0.6 x (1.6 x 10^{- 19})} = 2.8 x 10^{- 9} C / m ²

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An electron in a vacuum chamber is fired with a speed of $8300 k m / s$ toward a large, uniformly charged plate $75 c m$ away. The electron reaches a closest distance of $15 c m$ before being repelled. What is the plate’s surface charge density?

Short Answer

Step by step solution

Given information and formula used

Calculating the plate’s surface charge density

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An electron in a vacuum chamber is fired with a speed of 8300km/stoward a large, uniformly charged plate 75cm away. The electron reaches a closest distance of 15cm before being repelled. What is the plate’s surface charge density?

Short Answer

Step by step solution

Given information and formula used

Calculating the plate’s surface charge density

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Astrophysics

Radiation

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Famous Physicists

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Measurements

Study anywhere. Anytime. Across all devices.

An electron in a vacuum chamber is fired with a speed of $8300 k m / s$ toward a large, uniformly charged plate $75 c m$ away. The electron reaches a closest distance of $15 c m$ before being repelled. What is the plate’s surface charge density?