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Chapter 23: Q. 49 (page 655)

An infinite plane of charge with surface charge density $3.2 渭 C / m^{2}$ has a $20 - c m$ -diameter circular hole cut out of it. What is the electric field strength directly over the center of the hole at a distance of $12 c m$ ?
Hint: Can you create this charge distribution as a superposition of charge distributions for which you know the electric field?

Short Answer

Expert verified

Electrical field intensity directly over the middle of the outlet, $E_{total} = 1.4 脳 10^{5} \frac{N}{C}$

Step by step solution

01

Electric field

When energy is present in any form, an electrical field is linked with each point in space.

The worth of E, also known as field of force strength, force field intensity, or just the electrical field, expresses the magnitude and direction of the electrical field.

02

Given values

Surface charge density $畏 = 3.2 \frac{渭 C}{m^{2}}$

$蔚_{o} = 8.85 脳 10^{- 12} \frac{C^{2}}{N 脳 m^{2}}$

$r = 10 cm 鈫� 0.10 m$

diameter is $z = 12 cm 鈫� 0.12 m$

03

Find field strength

Electric field strength is,

$E_{total} = E_{p} + E_{d}$

$E_{total} = \frac{畏}{2 蔚_{o}} - \frac{畏}{2 蔚_{o}} [1 - \frac{z}{\sqrt{z^{2} + r^{2}}}]$

$E_{total} = \frac{畏}{2 蔚_{o}} [\frac{z}{\sqrt{z^{2} + r^{2}}}]$

$E_{total} = \frac{(3.2 脳 10^{- 6} \frac{C}{m^{2}})}{2 (8.85 脳 10^{- 12} \frac{C^{2}}{N 路 m^{2}})} [\frac{0.12 m}{\sqrt{(0.12 m)^{2} + (0.10 m)^{2}}}]$

$E_{total} = 1.4 脳 10^{5} \frac{N}{C}$

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Most popular questions from this chapter

You've hung two very large sheets of plastic facing each other with distance $d$ between them, as shown in $FIGURE EX 23.20$ . By rubbing them with wool and silk, you've managed to give one sheet a uniform surface charge density and the other a uni $畏_{1} = - 畏_{0}$ form surface charge density $畏_{2} = + 3 畏_{0}$ . What are the electric field vectors at points $1$ , $2$ and $3$ $?$

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE P $23.35$ ? Give your answer (a) in component form and (b) as a magnitude and angle measured cw or ccw (specify which) from the positive $x$ -axis.

A small object is released at point $3$ in the center of the capacitor in FIGURE $Q 23.11$ . For each situation, does the object move to the right, to the left, or remain in place? If it moves, does it accelerate or move at constant speed?

a. A positive object is released from rest.

b. A neutral but polarizable object is released from rest.

c. A negative object is released from rest.

A parallel-plate capacitor consists of two square plates, size $L 脳 L,$ separated by distance d. The plates are given charge $卤 Q$ . What is the ratio $E_{f} / E_{i}$ of the final to initial electric field strengths if

(a) Q is doubled,

(b)L is doubled, and

(c) d is doubled? Each part changes only one quantity; the other quantities have their initial values

A $10 - cm$ long thin glass rod uniformly charged to $+ 10 nC$ and a $10 - cm$ -long thin plastic rod uniformly charged to $- 10 nC$ are placed side by side, $4.0 cm$ apart. What are the electric field strengths $E_{1}$ to $E_{3}$ at distances $1.0 cm, 2.0 cm$ , and from the glass rod a $3.0 cm$ long the line connecting the midpoints of the two rods?

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