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Chapter 16: Q46P (page 626)

How much work is required to move a proton and an electron at rest a distance $3 脳 10^{- 8} m$ apart to be at rest a distance $7 脳 10^{- 8} m$ apart?

Short Answer

Expert verified

The work required to move the electron and proton is $4.3 脳 10^{- 21} J$ .

Step by step solution

01

Write the given data from the question.

Initial distance between electron and proton, $r_{1} = 3 脳 10^{- 8} m$

Final distance between electron and proton, $r_{2} = 7 脳 10^{- 8} m$

Charge on proton, $q_{1} = + 1.6 脳 10^{- 19} C$

Charge of electron, $q_{2} = - 1.6 脳 10^{- 19} C$

02

Determine the formulas to calculate the work required to move a proton and electron.

The expression to calculate the work required to move proton and electron is given as follows.

$W = 9 脳 10^{9} 脳 |q_{1} q_{2}| (\frac{1}{r_{2}} - \frac{1}{r_{1}})$ 鈥︹€� (i)

03

Calculate the work required to move a proton and electron.

Calculate the required work.

Substitute $3 脳 10^{- 8} m$ for $r_{1}$ , $1.6 脳 10^{- 19} C$ , for $q_{1}$ , $7 脳 10^{- 8} m$ for $r_{2}$ , and $- 1.6 脳 10^{- 19} C$ for $q_{2}$ into equation (i).

$W = 9 脳 10^{9} 脳 |1.6 脳 10^{- 19} 脳 (- 1.6 脳 10^{- 19})| (\frac{1}{3 脳 10^{- 8}} - \frac{1}{7 脳 10^{- 8}}) W = 9 脳 10^{9} 脳 \frac{2.56 脳 10^{- 38}}{10^{- 8}} (\frac{7 - 3}{3 脳 7}) W = 9 脳 2.56 脳 10^{- 21} 脳 \frac{4}{21} W = 4.3 脳 10^{- 21} J$

Hence the work required to move the electron and proton is $4.3 脳 10^{- 21} J$ .

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Most popular questions from this chapter

If throughout a particular region of space the potential can be expressed as $V = 4 x z + 2 y - 5 z$ , what are the vector components of the electric field at location $(x, y, z)$ ?

A particle with charge\( + {q_1}\)and a particle with charge\( - {q_2}\)are located as shown in figure 16.91. What is the potential (relative to infinity) at location A.

Locations $A = < a, 0, 0 > and B = < b, 0, 0 >$ are on the +x axis, as shown in Figure 16.61. Four possible expressions for the electric field along the x axis are given below. For each expression for the electric field, select the correct expression (1鈥�8) for the potential difference $V_{A} - V_{B}$ . In each case K is a numerical constant with appropriate units.

$(a) \overset{鈫�}{E} = < \frac{K}{x^{2}}, 0, 0 > (b) \overset{鈫�}{E} = < \frac{K}{x^{3}}, 0, 0 > (c) \overset{鈫�}{E} = < \frac{K}{x}, 0, 0 > (b) \overset{鈫�}{E} = < Kx, 0, 0 > (1) V_{A} - V_{B} = 0 (2) V_{A} - V_{B} = K (a - b) (3) V_{A} - V_{B} = K (\frac{1}{a} - \frac{1}{b}) (4) V_{A} - V_{B} = K (\frac{1}{a^{3}} a - \frac{1}{b^{3}} b) (5) V_{A} - V_{B} = \frac{1}{2} K (b^{2} - a^{2}) (6) V_{A} - V_{B} = K In (\frac{b}{a}) (7) V_{A} - V_{B} = K (a^{3} - b^{3}) (8) V_{A} - V_{B} = \frac{1}{2} K (\frac{1}{a^{2}} - \frac{1}{b^{2}})$

For a path starting at B and going to A (Figure 16.9), calculate (a) the change in electric potential, (b) the potential energy change for the system when a proton moves from B to A, and (c) the potential energy change for the system when an electron moves from B to A. For a path starting at B and going to C, calculate (d) the change in electric potential, (e) the potential energy change for the system when a proton moves from B to C, and (f) the potential energy change for the system when an electron moves from B to C.

The graph in Fig.16.56 shows the electric potential energy for a system of two interacting objects, as a function of the distance between the objects. What system might this graph represent?

(1) Two Protons, (2) Two sodium ions, (3) Two neutrons, (4) Two chloride ions, (5) Two electrons, (6) A Proton and an Electron, (7) A sodium ion and a chloride ion.

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