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Chapter 26: Q. 51 (page 739)

The potential at the center of a 4.0-cm-diameter copper sphere is 500 V, relative to V = 0 V at infinity. How much excess charge is on the sphere?

Short Answer

Expert verified

The excess charge is on the sphere is 1.1nC .

Step by step solution

01

Given Information

We have given that the potential at the center of a 4.0-cm-diameter copper sphere is 500 V, relative to V = 0 V at infinity.

02

Simplify

The sphere is conductive, the potential will be the same throughout the volume, and will be equal to the potential at the surface of the sphere. The potential created by charge

$V = \frac{k q}{r}$ ,

Where r is the given radius of the sphere. and solve for the charge as

localid="1648562464911" $q = \frac{V r}{k},$

Substituting radius with diameter

$q = \frac{V d}{2 k}$

Using the numerical values

localid="1649261072160" $q = \frac{500 \cdot 0.04}{2 \cdot 9 \cdot 10^{9}} = 1.1 n C$

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Most popular questions from this chapter

You need a capacitance of $50 m F$ , but you don’t 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?

Figure Q26.2 shows the electric potential as a function of $x$ . Draw a graph of $E_{x} versus x$ in this same region of space.

Figure EX26.4 is a graph of $E_{x}$ . The potential at the origin is $- 50 V$ . What is the potential at $x = 3.0 m$ ?

Consider a uniformly charged sphere of radius R and total cAlC charge Q. The electric field $E_{out}$ outside the sphere $(r \geq R)$ 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 $(r \leq R)$ is radially outward with field strength

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

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 $\leq$ r $\leq$ 3 R.

What are the magnitude and direction of the electric field at the dot in Figure EX26.7?

See all solutions

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