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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

FIGURE is a cross section of two infinite lines of charge that extend out of the page. The linear charge densities are $卤位$ . Find an expression for the electric field strength $E$ at height $y$ above the midpoint between the lines.

A small segment of wire in FIGURE $Q 23.4$ contains $10 n C$ of charge.

a. The segment is shrunk to one-third of its original length. What is the ratio of $位_{f} / 位_{i}$ , where $位_{i} a n d 位_{f}$ are the initial and final linear charge densities?

b. A proton is very far from the wire. What is the ratio Ff /Fi of the electric force on the proton after the segment is shrunk to the force before the segment was shrunk?

c. Suppose the original segment of wire is stretched to $10$ times its original length. How much charge must be added to the wire to keep the linear charge density unchanged?

A parallel-plate capacitor is formed from two $6.0$ - $c m$ -diameter electrodes spaced $2.0 m m$ apart. The electric field strength inside the capacitor is $1.0 脳 10^{6} N / C$ . What is the charge (in $n C$ ) on each electrode?

Two parallel plates $1.0 c m$ apart are equally and oppositely charged. An electron is released from rest at the surface of the negative plate and simultaneously a proton is released from rest at the surface of the positive plate. How far from the negative plate is the point at which the electron and proton pass each other?

A $12 - c m$ long thin rod has the nonuniform charge density $位 (x) = (2.0 nC / cm) e^{- | x | / (6.0 cm)}$ , where localid="1648623923714" $x$ is measured from the center of the rod. What is the total charge on the rod?

Hint: This exercise requires an integration. Think about how to handle the absolute value sign.

See all solutions

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