Q. 51 FIGURE P22.51聽shows four charge... [FREE SOLUTION]

91影视

Chapter 22: Q. 51 (page 626)

FIGURE $P 22.51$ shows four charges at the corners of a square of side $L$ . What is the magnitude of the net force on $q$ ?

Short Answer

Expert verified

Magnitude of net force on charge is $(2 - \sqrt{2}) \frac{KQq}{L^{2}}$ .

Step by step solution

Figure for magnitude of the net force on charge

Figure is,

Step 2:

Columns law for force is,

$F_{C} = F_{1 on 2} = F_{2 on 1} = \frac{K |q_{1}| |q_{2}|}{r^{2}}$

$L$ is the distance between $q_{1}$ andlocalid="1649103824153" $q$ :

$F_{q_{1} on q} = \frac{{Kq}_{1} q_{\hat{i}}}{L^{2}}$

$\sqrt{2} L$ is the distance between $q_{2}$ andlocalid="1649103830714" $q$ :

$F_{q_{2} on q} = \frac{{Kq}_{q}}{(\sqrt{2} L)^{2}} \cos 45^{o} \hat{i} + \frac{{Kq}_{2} q}{(\sqrt{2} L)^{2}} \sin 45^{o} \hat{j}$

$= (\frac{{Kq}_{2} q}{(\sqrt{2} L)^{2}}) (\frac{1}{\sqrt{2}}) \hat{i} + (\frac{{Kq}_{2} q}{(\sqrt{2} L)^{2}}) (\frac{1}{\sqrt{2}}) \hat{j}$

$= (\frac{K (4 Q) q}{(\sqrt{2} L)^{2}}) (\frac{1}{\sqrt{2}}) \hat{i} + (\frac{K (4 Q) q}{(\sqrt{2} L)^{2}}) (\frac{1}{\sqrt{2}}) \hat{j}$

$= (\frac{4 KQq}{2 \sqrt{2} L^{2}}) \hat{i} + (\frac{4 KQq}{2 \sqrt{2} L^{2}}) \hat{j}$

Calculation for net force on charge

$L$ is distance for $q_{3}$ and $q$ :

$F_{q_{3} on q} = \frac{{Kq}_{3} q}{L^{2}} \hat{j}$

$= \frac{- KQq}{L^{2}} \hat{j}$

Net force is,

$F_{net} = F_{q_{1} on q} + F_{q_{2} on q} + F_{q_{3} on q}$

$= \frac{- KQq}{L^{2}} \hat{i} + (\frac{4 KQq}{2 \sqrt{2} L^{2}}) \hat{i} + (\frac{4 KQq}{2 \sqrt{2} L^{2}}) \hat{j} + \frac{- KQq}{L^{2}} \hat{j}$

$= \frac{KQq}{L^{2}} [- 1 + \frac{2}{\sqrt{2}}] \hat{i} + \frac{KQq}{L^{2}} [- 1 + \frac{2}{\sqrt{2}}] \hat{j}$

Magnitude of net force is,

$F_{net} = \sqrt{{(\frac{KQq}{L^{2}} [- 1 + \frac{2}{\sqrt{2}}])}^{2} + {(\frac{KQq}{L^{2}} [- 1 + \frac{2}{\sqrt{2}}])}^{2}}$

$= \sqrt{2} (\frac{KQq}{L^{2}} [- 1 + \frac{2}{\sqrt{2}}])$

$= (2 - \sqrt{2}) \frac{KQq}{L^{2}}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

FIGURE $P 22.51$ shows four charges at the corners of a square of side $L$ . What is the magnitude of the net force on $q$ ?

Short Answer

Step by step solution

Figure for magnitude of the net force on charge

Step 2:

Calculation for net force on charge

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physics of Motion

Rotational Dynamics

Electrostatics

Modern Physics

Solid State Physics

Physical Quantities And Units

Study anywhere. Anytime. Across all devices.

91影视

FIGURE P22.51shows four charges at the corners of a square of side L. What is the magnitude of the net force onq?

Short Answer

Step by step solution

Figure for magnitude of the net force on charge

Step 2:

Calculation for net force on charge

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physics of Motion

Rotational Dynamics

Electrostatics

Modern Physics

Solid State Physics

Physical Quantities And Units

Study anywhere. Anytime. Across all devices.

FIGURE $P 22.51$ shows four charges at the corners of a square of side $L$ . What is the magnitude of the net force on $q$ ?