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Chapter 22: Q. 46 (page 626)

What is the force $\overset{鈫�}{F}$ on the $1.0 nC$ charge at the bottom in FIGURE $P 22.46$ $?$ Give your answer in component form.

Short Answer

Expert verified

Force on the $1.0 nC$ at the bottom is $1.02 脳 10^{- 5} \hat{i} + 2.2 脳 10^{- 5} \hat{j} N$ .

Step by step solution

01

Figure for force on the charge1.0 nC

Figure is,

02

Calculation of forceq2andq3

Force on charge $q_{2}$ :

${\overset{鈫�}{F}}_{2 on 1} = \frac{(9 脳 10^{9}) (1 脳 10^{- 9}) (2 脳 10^{- 9})}{{(5 脳 10^{- 2})}^{2}} [\cos 45 掳 \hat{i} + \sin 45 掳 \hat{j}]$

$= 0.72 脳 10^{- 5} N [\cos 45 掳 \hat{i} + \sin 45 掳 \hat{j}]$

Force on chargelocalid="1649091309769" $q_{3}$ :

localid="1649091320016" ${\overset{鈫�}{F}}_{3 on 1} = 2.16 脳 10^{- 5} N \hat{j}$

03

Calculation for force onq4andq1

Force on charge $q_{4}$ :

${\overset{鈫�}{F}}_{4 on 1} = (0.72 脳 10^{- 5} N) [\cos 45 掳 \hat{i} - \sin 45 掳 \hat{j}]$

Force on chargelocalid="1649091299979" role="math" $q_{1}$ :

${\overset{鈫�}{F}}_{on 1} = {\overset{鈫�}{F}}_{2 on 1} + {\overset{鈫�}{F}}_{3 on 1} + {\overset{鈫�}{F}}_{4 on 1}$

$= 2 (0.72 脳 10^{- 5} N) \cos (45 掳) \hat{i} + (2.16 脳 10^{- 5} N) \hat{j}$

$= 1.02 脳 10^{- 5} \hat{i} + 2.2 脳 10^{- 5} \hat{j} N$

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Most popular questions from this chapter

Can an insulator be charged? If so, how would you charge an insulator? If not, why not?

You have two neutral metal spheres on wood stands. Devise a procedure for charging the spheres so that they will have opposite charges of exactly equal magnitude. Use charge diagrams to explain your procedure.

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a. Have electrons been removed from the rod or protons added?

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Can a conductor be charged? If so, how would you charge a conductor? If not, why not?

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