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Chapter 22: Q. 45 (page 626)

What is the force $\overset{鈫�}{F}$ on the $1.0 nC$ charge at the bottom in FIGURE $P 22.45$ $?$ Give your answer in component form.

Short Answer

Expert verified

Force on $1.0 nC$ is ${\overset{鈫�}{F}}_{on 1} = 1.1 脳 10^{- 5} \hat{j} N$ .

Step by step solution

01

Figure for force on the1.0 nccharge

Figure is,

02

Calculation of force on q2andq3

Putting a charge of $1.0 nC$ at the origin and labelling it $q_{1}$ .

For charge $q_{2}$ :

${\overset{鈫�}{F}}_{2} on 1 = \frac{{kq}_{1} q_{2}}{r^{2}} \hat{i}$

$= \frac{(9 脳 10^{9}) (1 脳 10^{- 9}) (2 脳 10^{- 9})}{{(5 脳 10^{- 2})}^{2}} [- \cos 45 掳 \hat{i} - \sin (45 掳) \hat{j}]$

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

For chargelocalid="1649089752680" $q_{3}$ :

${\overset{鈫�}{F}}_{3 on 1} = \frac{(9 脳 10^{9}) (1 脳 10^{- 9}) (6 脳 10^{- 9})}{{(5 脳 10^{- 2})}^{2}} \hat{j} N$

$= 2.16 脳 10^{- 5} \hat{j} N$

03

Force for chargeq4andq1

For charge $q_{4}$ :

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

For charge $q_{1}$ :

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

${\overset{鈫�}{F}}_{on 1} = 1.1 脳 10^{- 5} \hat{j} N$

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Most popular questions from this chapter

The electric field 2.0 cm from a small object points away from the object with a strength of 270,000 N/C. What is the object鈥檚 charge?

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d. What is the magnitude of the electron鈥檚 acceleration?

Linear accelerator uses alternating electric fields to accelerate electrons to close to the speed of light. A small number of the electrons collide with a target, but a large majority pass through the target and impact a beam dump at the end of the accelerator. In one experiment the beam dump measured charge accumulating at a rate of -2.0 nC/s. How many electrons traveled down the accelerator during the 2.0 h run?

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