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Chapter 26: Q. 3 (page 736)

a. Suppose that $\overset{鈫�}{E} = \overset{鈫�}{0} V / m$ throughout some region of space. Can you conclude that $V = 0 V$ in this region? Explain.
b. Suppose that $V = 0 V$ throughout some region of space. Can you conclude that $\overset{鈫�}{E} = \overset{鈫�}{0} V / m$ in this region? Explain.

Short Answer

Expert verified

(a) No, $v$ is not necessarily $0$ .

(b) Yes, $\overset{鈫�}{| E |}$ is zero

Step by step solution

01

Given information and formula used

Given :

a. $\overset{鈫�}{E} = \overset{鈫�}{0} V / m$

b. $V = 0 V$

Theory used :

In the region of constant electric potential, electric field is zero so there is no charge inside the region.

Electric field is the negative slope (鈥渄erivative鈥� or 鈥済radient鈥�) of the potential.

$\overset{鈫�}{E} = 鈭� \frac{螖 V}{螖 x}$

02

Determining if V = 0 Vin this region

a) No.

However, you can deduce that $鈭� V = 0 V$ , implying that the potential in that region of space is constant.

03

Determining if E→= 0→ V/m

(b) The answer is yes.

Because $\overset{鈫�}{E} = 鈭� \frac{螖 V}{螖 x}$ , when $V$ is constant in a region of space, $E = 0 V / m$ .

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Most popular questions from this chapter

You need a capacitance of $50 m F$ , but you don鈥檛 happen to have a $50 m F$ capacitor. You do have a $75 m F$ capacitor. What additional capacitor do you need to produce a total capacitance of $50 m F$ ? Should you join the two capacitors in parallel or in series?

A capacitor being charged has a current carrying charge to and away from the plates. In the next chapter we will define current to be $d Q / d t$ the rate of charge flow. What is the current to a $10 渭 F$ capacitor whose voltage is increasing at the rate of $2.0 V / s$ ?

A battery with an emf of $60 V$ is connected to the two capacitors shown in FIGURE $P 26.62$ . Afterward, the charge on capacitor $2$ is $450 渭 C$ . What is the capacitance of capacitor $2$ ?

Consider a uniformly charged sphere of radius R and total cAlC charge Q. The electric field $E_{out}$ outside the sphere $(r 鈮� R)$ is simply that of a point charge Q. In Chapter 24, we used Gauss's law to find that the electric field $E_{in}$ inside the sphere $(r 鈮� R)$ is radially outward with field strength

$E_{in} = \frac{1}{4 蟺系_{0}} \frac{Q}{R^{3}} r$

a. The electric potential $V_{out}$ outside the sphere is that of a point charge Q. Find an expression for the electric potential $V_{in}$ at position r inside the sphere. As a reference, let $V_{in} = V_{out}$ at the surface of the sphere.

b. What is the ratio $V_{center} / V_{surface} ?$

c. Graph V versus r for 0 $鈮�$ r $鈮�$ 3 R.

An ideal parallel-plate capacitor has a uniform electric field between the plates, zero-field outside. By superposition, half the field strength is due to one plate and a half due to the other.

a. The plates of a parallel-plate capacitor are oppositely charged and attract each other. Find an expression in terms of $C, 鈭� V_{c}$ and the plate separation $d$ for the force one plate exerts on the other.

b. What is the attractive force on each plate of a $100 pF$ capacitor with a plate spacing when $1.0 mm$ charged to $1000 V$ ?

See all solutions

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