Chapter 22: Q. 45 (page 626)

What is the force $\vec{F}$ 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 ${\vec{F}}_{on 1} = 1.1 \times 10^{- 5} \hat{j} N$ .

Step by step solution

Figure for force on the1.0 nccharge

Figure is,

Calculation of force on q2andq3

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

For charge $q_{2}$ :

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

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

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

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

${\vec{F}}_{3 on 1} = \frac{(9 \times 10^{9}) (1 \times 10^{- 9}) (6 \times 10^{- 9})}{{(5 \times 10^{- 2})}^{2}} \hat{j} N$

$= 2.16 \times 10^{- 5} \hat{j} N$

Force for chargeq4andq1

For charge $q_{4}$ :

${\vec{F}}_{4 on 1} = 0.72 \times 10^{- 5} N [\cos 45 ° \hat{i} - \sin 45 ° \hat{j}]$

For charge $q_{1}$ :

${\vec{F}}_{on 1} = {\vec{F}}_{2 on 1} + {\vec{F}}_{3 on 1} + {\vec{F}}_{4 on 1}$

${\vec{F}}_{on 1} = 1.1 \times 10^{- 5} \hat{j} N$

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

Short Answer

Step by step solution

Figure for force on the1.0 nccharge

Calculation of force on q2andq3

Force for chargeq4andq1

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What is the forceF→on the1.0nCcharge at the bottom in FIGURE P22.45?Give your answer in component form.

Short Answer

Step by step solution

Figure for force on the1.0 nccharge

Calculation of force on q2andq3

Force for chargeq4andq1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Astrophysics

Electric Charge Field and Potential

Linear Momentum

Oscillations

Classical Mechanics

Study anywhere. Anytime. Across all devices.

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