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Chapter 26: Q. 5 (page 737)

a. Which point in Figure EX26.5, 'A' or 'B', has a larger electric potential?
b. What is the potential difference between 'A' and 'B'?

Short Answer

Expert verified

a. The point 'A' in Figure EX26.5has a larger electric potential.

b. The potential difference between 'A' and 'B' is $- 70 V$

Step by step solution

01

Given information and formula used

Given figure :

Theory used :

1) Electric field lines point from high to low potential.

2) $鈭� V = - E 路 d x$

02

Evaluating which point has a larger electric potential and the potential difference between 'A' and 'B'

(a) 'A' has a bigger potential than 'B' because the electric field lines point from high to low potential.

So, $V_{A} > V_{B}$

(b) The potential difference between 'A' and 'B' is :

role="math" localid="1649498158410" $鈭� V = - E 路 d x 鈬� V_{B} - V_{A} = - 1000 脳 7 脳 10^{- 2} = - 70 V$

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Most popular questions from this chapter

What is the potential difference between $x_{i} = 10 c m$ and $x_{f} = 30 c m$ in the uniform electric field $E_{x} = 1000 V / m$ ?

A nerve cell in its resting state has a membrane potential of $- 70 mV$ , meaning that the potential inside the cell is $70 mV$ less than the potential outside due to a layer of negative charge on the inner surface of the cell wall and a layer of positive charge on the outer surface. This effectively makes the cell wall a charged capacitor. When the nerve cell fires, sodium ions, ${Na}^{+}$ , flood through the cell wall to briefly switch the membrane potential to $+ 40 mV$ . Model the central body of a nerve cell-the soma-as a $50 渭 m$ diameter sphere with a $7.0 - nm$ -thick cell wall whose dielectric constant is 9.0. Because a cell's diameter is much larger than the wall thickness, it is reasonable to ignore the curvature of the cell and think of it as a parallel-plate capacitor. How many sodium ions enter the cell as it fires?

An infinitely long cylinder of radius $R$ has linear charge density $I$ . The potential on the surface of the cylinder is $V_{0}$ , and the electric field outside the cylinder is localid="1648568519666" $E_{r} = 位 / 2 蟺 {鈭�}_{0} r$ . Find the potential relative to the surface at a point that is distance r from the axis, assuming localid="1648568540457" $r > R$ .

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.

Figure EX26.9shows a graph of $V versus x$ in a region of space. The potential is independent of y and z. What is $E_{x}$ at

(a) $x = - 2 c m$ , (b) $x = 0 c m$ , and (c) $x = 2 c m$ ?

See all solutions

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