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Chapter 23: Q. 5 (page 653)

An electric dipole is formed from two charges, $卤 q$ , spaced $1.0 c m$ apart. The dipole is at the origin, oriented along the y-axis. The electric field strength at the point $(x, y) = (0 c m, 10 c m)$ is $360 N / C$ .
a. What is the charge q? Give your answer in $n C$ .
b. What is the electric field strength at the point $(x, y) = (10 c m, 0 c m)$ ?

Short Answer

Expert verified

(a) The charge q is $2.003 脳 10^{- 11} C$ .

(b) The electric field strength is $8.96 N / C$

Step by step solution

01

Given information (part a)

Coordinates

$+ q = (0, 0.5) c m - q = (0, 0.5) c m E = 360 N / C$

02

Explanation (part a)

The electric field due to a dipole is given by

$E = p / 2 蟺蔚 y^{3}$ Where P=dipole moment and r= distance of dipole to point of electric field=10cm=0.10m. E=electric field strength at (0,10)=360N/C.

So, role="math" localid="1648660696169" $E = p / 2 蟺蔚 r^{3}$

role="math" localid="1648660707891"

p = 2 蟺 蔚 r^{3} E = 2 蟺 脳 8.854 脳 10^{- 12} 脳 (0.10 m)^{3} 脳 360 N / C = 2.003 脳 10^{- 13} Cm

$q = \frac{蚁}{d} = \frac{2.003 脳 10^{- 13} C m}{0.01 m} = 2.003 脳 10^{- 11} C$

03

Given information (part b)

$+ q = (0, 0.5) c m - q = (0, 0.5) c m E = 360 N / C$

04

Explanation (part b)

The electric field at the perpendicular axis $(10, 0)$ :

$E = \frac{q 脳 x}{{蟺系}_{0} \sqrt{{(d^{2} + 4 x^{2})}^{3}}} = \frac{(2.003 脳 10^{- 11} C) 脳 0.10 m}{蟺脳 8.854 脳 10^{- 12} \sqrt{{(0 . 01^{2} + 4 脳 (0.1)^{2})}^{3}}} = 8.96 N / C$

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Most popular questions from this chapter

A problem of practical interest is to make a beam of electrons turn a $90 掳$ corner. This can be done with the parallel-plate capacitor shown in FIGURE. An electron with kinetic energy $3.0 脳 10^{- 17} J$ enters through a small hole in the bottom plate of the capacitor.

a. Should the bottom plate be charged positive or negative relative to the top plate if you want the electron to turn to the right? Explain.

b. What strength electric field is needed if the electron is to emerge from an exit hole $1.0 c m$ away from the entrance hole, traveling at right angles to its original direction?

Hint: The difficulty of this problem depends on how you choose your coordinate system.

c. What minimum separation $d_{\min}$ must the capacitor plates have?

FIGURE shows a thin rod of length $L$ with total charge $Q$ .

a. Find an expression for the electric field strength at point $P$ on the axis of the rod at distance $r$ from the center.

b. Verify that your expression has the expected behavior if $r 鈮� L$ .

c. Evaluate $E$ at $r = 3.0 c m$ if $L = 5.0 c m$ and $Q = 3.0 nC$ .

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE EX23.2? Specify the direction as an angle above or below horizontal.

Air "breaks down" when the electric field strength reaches $3.0 脳 10^{6} N / c$ , causing a spark. A parallel-plate capacitor is made from two $4.0 c m 脳 4.0 c m$ electrodes. How many electrons must be transferred from one electrode to the other to create a spark between the electrodes?

Two $10 cm$ diameter charged rings face each other, $20 cm$ apart. Both rings are charged to $+ 20 nC$ . What is the electric field strength at (a) the midpoint between the two rings and (b) the center of the left ring?

See all solutions

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