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Chapter 23: Q. 31 (page 654)

A $1.0 - m m$ -diameter oil droplet (density role="math" localid="1649088632675" $900 k g / m^{3}$ ) is negatively charged with the addition of $25$ extra electrons. It is released from rest $2.0 m m$ from a very wide plane of positive charge, after which it accelerates toward the plane and collides with a speed of $3.5 m / s$ . What is the surface charge density of the plane?

Short Answer

Expert verified

The surface charge density of the plane is $6.4 x 10^{- 6} C / m 虏$

Step by step solution

01

Given information and formula used

Given :

Diameter of oil droplet : $1.0 - m m$

Density : $900 k g / m^{3}$

Charge : Negatively charged with $25$ extra electrons.

It is released from rest : $2.0 m m$

Collides with a speed of : $3.5 m / s$ .

Theory used :

Conservation of Energy says :

$\frac{1}{2} m v^{2} = q E d$

02

Calculating the surface charge density of the plane

Mass of the droplet is :

$蚁脳 \frac{4}{3} {蟺谤}^{3} = 900 脳 \frac{4}{3} 蟺脳 {(0.5 脳 10^{- 6})}^{3} = 4.7 x 10^{- 16} k g$

Mass charge on the droplet :

$n e = 25 脳 1.6 脳 10^{- 19} = 40 脳 10^{- 19} C$

From energy conservation :

$E = \frac{1}{2} 脳 \frac{m v 虏}{q d} = \frac{1}{2} 脳 \frac{4.7 脳 10^{- 16} 脳 {(3.5)}^{2}}{40 脳 10^{- 19} 脳 2 脳 10^{- 3}} = 3.6 x 10^{5} N / C$

We know that for electric field owing to infinite plane sheet:

$E = \frac{畏}{2 蔚_{0}} 鈬� 畏 = E 2 蔚_{0} = 2 脳 8.85 脳 10^{- 12} 脳 3.6 脳 10^{5} = 6.4 x 10^{- 6} C / m 虏$

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Most popular questions from this chapter

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?

Two $10 cm$ diameter charged rings face each other, $20 cm$ apart. Both rings are charged to $+ 20 nC$ . What is the electric field strength at (a) the midpoint between the two rings and (b) the center of the left ring?

You鈥檝e been assigned the task of determining the magnitude and direction of the electric field at a point in space. Give a step-by-step procedure of how you will do so. List any objects you will use, any measurements you will make, and any calculations you will need to perform. Make sure that your measurements do not disturb the charges that are creating the field.

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?

FIGURE P25.69 shows a thin rod of length L and charge Q. Find an expression for the electric potential a distance x away from the center of the rod on the axis of the rod.

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