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Chapter 23: Q. 29 (page 654)

The surface charge density on an infinite charged plane is $- 2.0 脳 10^{- 6} C / m^{2}$ . A proton is shot straight away from the plane at $2.0 脳 10^{6} m / s$ . How far does the proton travel before reaching its turning point?

Short Answer

Expert verified

The proton travels $18 c m$ before reaching its turning point .

Step by step solution

01

Given information and formula used

Given :

The surface charge density on the infinite charged plane : $- 2.0 脳 10^{- 6} C / m^{2}$

Proton shot straight away at the speed : $2.0 脳 10^{6} m / s$

Theory used :

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

$E = \frac{蟽}{2 蔚_{0}}$

Newton's law :

$\frac{1}{2} m ({(v_{f})}^{2} 鈥� {(v_{i})}^{2}) = q E d$

02

Calculating how far the proton travels before reaching its turning point

Due to the action of the infinite plane's electric field, this proton will come to a halt before returning. We can compute the distance it goes before turning back using conservation of energy :

$\frac{1}{2} m ({(v_{f})}^{2} 鈥� {(v_{i})}^{2}) = q E d 鈬� d = \frac{m ({(v_{f})}^{2} 鈥� {(v_{i})}^{2})}{2 q E} = \frac{m ({(v_{f})}^{2} 鈥� {(v_{i})}^{2})}{2 q (蟽 / 2 蔚_{0})} = \frac{(1.67 x 10^{- 27} k g) (0 - {(2.0 x 10^{6} m / s)}^{2}) (8.854 x 10^{- 12} C^{2} / N 路 m^{2})}{(1.6 x 10^{- 19} C) (2.0 x 10^{- 6} C / m^{2})} 鈬� d = 18 c m$

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Most popular questions from this chapter

One type of ink-jet printer, called an electrostatic ink-jet printer, forms the letters by using deflecting electrodes to steer charged ink drops up and down vertically as the ink jet sweeps horizontally across the page. The ink jet forms $30 渭 m$ diameter drops of ink, charges them by spraying $800, 000$ electrons on the surface, and shoots them toward the page at a speed of $20 m / s$ . Along the way, the drops pass through two horizontal, parallel electrodes that are $6.0 m m long, 4.0 m m$ wide, and spaced $1.0 m m$ apart. The distance from the center of the electrodes to the paper is $2.0 c m$ . To form the tallest letters, which have a height of $6.0 m m$ , the drops need to be deflected upward (or downward) by $3.0 m m$ . What electric field strength is needed between the electrodes to achieve this deflection? Ink, which consists of dye particles suspended in alcohol, has a density of $800 k g / m^{3}$ .

A $12 - c m$ long thin rod has the nonuniform charge density $位 (x) = (2.0 nC / cm) e^{- | x | / (6.0 cm)}$ , where localid="1648623923714" $x$ is measured from the center of the rod. What is the total charge on the rod?

Hint: This exercise requires an integration. Think about how to handle the absolute value sign.

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?

The permanent electric dipole moment of the water molecule $(H_{2} O)$ is $6.2 脳 10^{- 30} Cm$ . What is the maximum possible torque on a water molecule in a $5.0 脳 10^{8} N / C$ electric field?

An electret is similar to a magnet, but rather than being permanently magnetized, it has a permanent electric dipole moment. Suppose a small electret with electric dipole moment $1.0 脳 10^{- 7} C m$ is $25 c m$ from a small ball charged to $+ 25 n C$ , with the ball on the axis of the electric dipole. What is the magnitude of the electric force on the ball?

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