Chapter 23: Q.52 (page 656)

An electron is launched at a $45^{鈭�}$ angle and a speed of $5.0 脳 10^{6} m / s$ from the positive plate of the parallel-plate capacitor shown in FIGURE P $23.52$ . The electron lands $4.0 cm$ away.
a. What is the electric field strength inside the capacitor?
b. What is the smallest possible spacing between the plates?

Short Answer

Expert verified

a. The electric field strength inside the capacitor is $a = 6.3 脳 10^{14} m / s^{2}$

b. The smallest possible spacing between the plates is

$E = 3.6 脳 10^{3} N / C$

$H = 1 cm$

Step by step solution

Velocity (part a)

The pace as in downward motion $V_{o} \cos 鈦� 45^{鈭�}$ .

And there is no stress with in downward motion

so,

d = V_{o} \cos 鈦� 45^{鈭�} 脳 t

$t = \frac{d}{V_{o} \cos 鈦� 45^{鈭�}}$

localid="1650219090644" $= \frac{4 脳 10^{鈭� 2} m 脳 \sqrt{2}}{5 脳 10^{6} m / s 脳 1}$

$= 1.13 脳 10^{鈭� 8} s$

At its highest point (vertical direction).

$v_{f} = 0$

$v = u 鈭� a t^{鈥�}$ $[t^{鈥�} = \frac{t}{2} = 0.56 脳 10^{鈭� 8} s (a opposite to Force)]$

$a = \frac{u}{a^{鈥�}}$

$= \frac{V_{o} \sin 鈦� 胃}{t^{鈥�}}$

localid="1650219122312" $= \frac{5 脳 10^{6} m / s}{\sqrt{2} 脳 0.56 脳 10^{鈭� 8} s}$

$a = 6.3 脳 10^{14} m / s^{2}$

Force (part b)

Force is,

e E = m a

$m a = e E ~ E$

$= \frac{m a}{e}$

localid="1650219349035" role="math" $= \frac{9.11 脳 10^{鈭� 31} k g 脳 6.3 脳 10^{14} m / s^{2}}{1.6 脳 10^{鈭� 19} C}$

$E = 3.6 脳 10^{3} N / C$

$Maximum H$

$v^{2} = u_{v}^{2} 鈭� 2 a H$

$H = \frac{u_{v}^{2}}{2 a}$

localid="1650219390403" $= \frac{{(\frac{5}{\sqrt{2}} 脳 10^{6})}^{2}}{2 脳 6.3 脳 10^{14} m / s^{2}}$

$= 1 脳 10^{鈭� 2} m$

$H = 1 cm$

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Short Answer

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Velocity (part a)

Force (part b)

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91影视

An electron is launched at a 45鈭�angle and a speed of 5.0脳106m/sfrom the positive plate of the parallel-plate capacitor shown in FIGURE P23.52. The electron lands 4.0cmaway.a. What is the electric field strength inside the capacitor?b. What is the smallest possible spacing between the plates?

Short Answer

Step by step solution

Velocity (part a)

Force (part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Electromagnetism

Force

Translational Dynamics

Waves Physics

Linear Momentum

Study anywhere. Anytime. Across all devices.