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Chapter 26: Q. 2 (page 737)

What is the potential difference between $y_{i} = - 5 c m$ and $y_{f} = 5 c m$ in the uniform electric field $\overset{鈫�}{E} = (120, 000 \hat{i} - 50, 000 \hat{j}) V / m$ ?

Short Answer

Expert verified

The potential difference is $5 k V$

Step by step solution

01

Given information and formula used

Given :

$y_{i} = - 5 c m$ ; and $y_{f} = 5 c m$

Uniform electric field : $\overset{鈫�}{E} = (120, 000 \hat{i} - 50, 000 \hat{j}) V / m$

Formula used :

$鈭� V = - 鈭� y 路 E_{y}$

02

Calculating the required the potential difference

We'll assume the $x$ -component of the position is the same for both positions because we don't know anything about it; for example, both positions are measured along the $y$ -axis.

$鈭� y = 0.05 - (- 0.05) = 0.1 m$ will be the difference in the $y$ -component.

With this knowledge, the potential difference will be :

$鈭� V = - 鈭� y 路 E_{y} = - 0.1 (- 50000) = 5000 V$

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Most popular questions from this chapter

a. Find an expression for the capacitance of a spherical capacitor, consisting of concentric spherical shells of radii $R_{1}$ (inner shell) and $R_{2}$ (outer shell).

b. A spherical capacitor with a $1.0 mm$ gap between the shells has a capacitance of $100 pF$ . What are the diameters of the two spheres?

An electric dipole at the origin consists of two charges q spaced apart along the y-axis.

a. Find an expression for the potential V(x, y) at an arbitrary point in the xy-plane. Your answer will be in terms of q, s, x, and y.

b. Use the binomial approximation to simplify your result from part a when s V x and s V y.

c. Assuming s V x and y, find expressions for Ex and Ey, the components of E u for a dipole.

d. What is the on-axis field E? Does your result agree with Equation 23.10?

e. What is the field E u on the bisecting axis? Does your result agree with Equation 23.11?

The two metal spheres in Figure Q26.9 are connected by a metal wire with a switch in the middle. Initially the switch is open. Sphere 1, with the larger radius, is given a positive charge. Sphere 2, with the smaller radius, is neutral. Then the switch is closed. Afterward, sphere 1 has charge $Q_{1}$ , is at potential $V_{1}$ , and the electric field strength at its surface is $E_{1}$ . The values for sphere 2 are $Q_{2}, V_{2}, and E_{2}$ .

a. Is $V_{1}$ larger than, smaller than, or equal to $V_{2}$ ? Explain.

b. Is $Q_{1}$ larger than, smaller than, or equal to $Q_{2}$ ? Explain.

c. Is $E_{1}$ larger than, smaller than, or equal to $E_{2}$ ? Explain.

The electric potential is $40 V$ at point A near a uniformly charged sphere. At point B, $2.0 渭 m$ farther away from the sphere, the potential has decreased by 0.16 mV. How far is point A from the center of the sphere?

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" $r > R$ .

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