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

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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,

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

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

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

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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

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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

Space Physics

Electromagnetism

Fluids

Dynamics

Magnetism and Electromagnetic Induction

Classical Mechanics

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 $q$ ?