Chapter 21: Q70P (page 609)

In Fig. 21-25, four particles form a square. The charges are $q_{1} =+Q$ , $q_{2} {=q}_{3} =q$ , and $q_{4} =-2.00Q$ . What is $\frac{q}{Q}$ if the net electrostatic force on particle 1 is zero?

Short Answer

Expert verified

The value of the net electrostatic force is $\frac{q}{Q} = \frac{1}{\sqrt{2}} = 0.707$ .

Step by step solution

Given

The given data $q_{1} = + Q, q_{2} = q_{3} = q,$ and $q_{4} = - 2.00 Q$

Calculate qQif the net electrostatic force on particle 1 is zero

For the net force on $q_{1} = + Q$ to vanish, the x force component due tomust

exactly cancel the force of attraction caused by $q_{4} = - 2.00 Q$ . Consequently,

$\begin{matrix} \frac{Q q}{4 π ε_{0} a^{2}} = \frac{Q | 2 Q |}{4 π ε_{0} {(\sqrt{2} a)}^{2}} c o s (45 °) \\ = \frac{Q^{2}}{4 π ε_{0} \sqrt{2} a^{2}} \end{matrix}$

or $q = \frac{Q}{\sqrt{2}}$

This implies that :

$\begin{matrix} \frac{q}{Q} = \frac{1}{\sqrt{2}} \\ = 0.707 \end{matrix}$

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In Fig. 21-25, four particles form a square. The charges are $q_{1} =+Q$ , $q_{2} {=q}_{3} =q$ , and $q_{4} =-2.00Q$ . What is $\frac{q}{Q}$ if the net electrostatic force on particle 1 is zero?

Short Answer

Step by step solution

Given

Calculate qQif the net electrostatic force on particle 1 is zero

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In Fig. 21-25, four particles form a square. The charges areq1=+Q,q2=q3=q, andq4=-2.00Q. What is qQif the net electrostatic force on particle 1 is zero?

Short Answer

Step by step solution

Given

Calculate qQif the net electrostatic force on particle 1 is zero

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Waves Physics

Linear Momentum

Force

Further Mechanics and Thermal Physics

Measurements

Astrophysics

Study anywhere. Anytime. Across all devices.

In Fig. 21-25, four particles form a square. The charges are $q_{1} =+Q$ , $q_{2} {=q}_{3} =q$ , and $q_{4} =-2.00Q$ . What is $\frac{q}{Q}$ if the net electrostatic force on particle 1 is zero?