Chapter 3: Q3.7P (page 129)

Find the force on the charge $+ q$ in Fig. 3.14. (The $x y$ plane is a grounded conductor.)

Short Answer

Expert verified

Answer

The net force on q is $- \frac{1}{4 {πε}_{0}} (\frac{29^{2}}{72 d^{2}}) z$ .

Step by step solution

Given data

Consider the given figure as shown below.

Here, from the given figure it is clear that $x y$ plane is grounded conductor, thus potential is zero

Determine force

As $+ q$ induces an equal and opposite charge of $- q$ at a distance of $Z = - 3 d$ and $- 2 q$ induces $+ 2 q$ at distance of $Z = - d$ .

Write the expression for force on $+ q$ due to $- 2 q$ ,.

$F_{1} = \frac{1}{4 π ε_{0}} \frac{q (- 2 q)}{{(2 d)}^{2}} z$ …… (1)

Write the expression for force on $+ q$ due to $+ 2 q$ ,.

$F_{1} = \frac{1}{4 {πε}_{0}} \frac{q (- 2 q)}{{(4 d)}^{2}} z$ …… (2)

Write the expression for force on $+ q$ due to $- q$ .

$F_{1} = \frac{1}{4 {πε}_{0}} \frac{q (- 2 q)}{{(6 d)}^{2}} z$ …… (3)

Determine the net force

Write the expression for the net force on q .

$F = F_{1} + F_{2} + F_{3} = \frac{q}{4 π ε_{0}} [\frac{- 2 q}{{(2 d)}^{2}} + \frac{2 q}{{(4 d)}^{2}} + \frac{- q}{{(6 d)}^{2}}] z = \frac{q^{2}}{4 π ε_{0}} [\frac{- 1}{2} + \frac{1}{8} - \frac{1}{36}] z = \frac{q^{2}}{4 π ε_{0}} (\frac{29 q^{2}}{72 d^{2}}) z$

Thus, the net force on q is $- \frac{q^{2}}{4 {πε}_{0}} (\frac{29 q^{2}}{72 d^{2}}) z$ .

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Find the force on the charge $+ q$ in Fig. 3.14. (The $x y$ plane is a grounded conductor.)

Short Answer

Step by step solution

Given data

Determine force

Determine the net force

One App. One Place for Learning.

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Find the force on the charge +qin Fig. 3.14. (The xyplane is a grounded conductor.)

Short Answer

Step by step solution

Given data

Determine force

Determine the net force

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Radiation

Astrophysics

Electromagnetism

Torque and Rotational Motion

Physical Quantities And Units

Kinematics Physics

Study anywhere. Anytime. Across all devices.

Find the force on the charge $+ q$ in Fig. 3.14. (The $x y$ plane is a grounded conductor.)