Chapter 22: Q. 46 (page 626)

What is the force $\vec{F}$ 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 $1.02 \times 10^{- 5} \hat{i} + 2.2 \times 10^{- 5} \hat{j} N$ .

Step by step solution

Figure for force on the charge1.0 nC

Figure is,

Calculation of forceq2andq3

Force on charge $q_{2}$ :

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

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

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

localid="1649091320016" ${\vec{F}}_{3 on 1} = 2.16 \times 10^{- 5} N \hat{j}$

Calculation for force onq4andq1

Force on charge $q_{4}$ :

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

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

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

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

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

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

Short Answer

Step by step solution

Figure for force on the charge1.0 nC

Calculation of forceq2andq3

Calculation for force onq4andq1

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What is the forceF→on the1.0nCcharge at the bottom in FIGURE P22.46?Give your answer in component form.

Short Answer

Step by step solution

Figure for force on the charge1.0 nC

Calculation of forceq2andq3

Calculation for force onq4andq1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Scientific Method Physics

Fluids

Electromagnetism

Space Physics

Electric Charge Field and Potential

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

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