# 18.6 Electric field lines: multiple charges  (Page 4/8)

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## Test prep for ap courses

An electric dipole (with +2 q and –2 q as the two charges) is shown in the figure above. A third charge, − q is placed equidistant from the dipole charges. What will be the direction of the net force on the third charge?

Four objects, each with charge + q , are held fixed on a square with sides of length d , as shown in the figure. Objects X and Z are at the midpoints of the sides of the square. The electrostatic force exerted by object W on object X is F . Use this information to answer questions 39–40.

What is the magnitude of force exerted by object W on Z ?

1. F /7
2. F /5
3. F /3
4. F /2

(b)

What is the magnitude of the net force exerted on object X by objects W , Y , and Z ?

1. F /4
2. F /2
3. 9 F /4
4. 3 F

The figure above represents the electric field in the vicinity of three small charged objects, R , S , and T . The objects have charges − q , +2 q , and − q , respectively, and are located on the x -axis at − d , 0, and d . Field vectors of very large magnitude are omitted for clarity.

(a) i) Briefly describe the characteristics of the field diagram that indicate that the sign of the charges of objects R and T is negative and that the sign of the charge of object S is positive.

ii) Briefly describe the characteristics of the field diagram that indicate that the magnitudes of the charges of objects R and T are equal and that the magnitude of the charge of object S is about twice that of objects R and T .

For the following parts, an electric field directed to the right is defined to be positive.

(b) On the axes below, sketch a graph of the electric field E along the x -axis as a function of position x .

(c) Write an expression for the electric field E along the x -axis as a function of position x in the region between objects S and T in terms of q , d , and fundamental constants, as appropriate.

(d) Your classmate tells you there is a point between S and T where the electric field is zero. Determine whether this statement is true, and explain your reasoning using two of the representations from parts (a), (b), or (c).

(a) i) Field vectors near objects point toward negatively charged objects and away from positively charged objects.

(a) ii) The vectors closest to R and T are about the same length and start at about the same distance. We have that ${q}_{R}/{d}^{2}={q}_{T}/{d}^{2}$ , so the charge on R is about the same as the charge on T . The closest vectors around S are about the same length as those around R and T . The vectors near S start at about 6 units away, while vectors near R and T start at about 4 units. We have that ${q}_{R}/{d}^{2}={q}_{S}/{D}^{2}$ , so ${q}_{S}/{q}_{R}={D}^{2}/{d}^{2}=36/16=2.25$ , and so the charge on S is about twice that on R and T .

(b)

(c)

$E=k\left[-\frac{q}{{\left(d+x\right)}^{2}}+\frac{2q}{{\left(x\right)}^{2}}+\frac{q}{{\left(d-x\right)}^{2}}\right]$

(d) The statement is not true. The vector diagram shows field vectors in this region with nonzero length, and the vectors not shown have even greater lengths. The equation in part (c) shows that, when $0 , the denominator of the negative term is always greater than the denominator of the third term, but the numerator is the same. So the negative term always has a smaller magnitude than the third term and since the second term is positive the sum of the terms is always positive.

## Section summary

• Drawings of electric field lines are useful visual tools. The properties of electric field lines for any charge distribution are that:
• Field lines must begin on positive charges and terminate on negative charges, or at infinity in the hypothetical case of isolated charges.
• The number of field lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.
• The strength of the field is proportional to the closeness of the field lines—more precisely, it is proportional to the number of lines per unit area perpendicular to the lines.
• The direction of the electric field is tangent to the field line at any point in space.
• Field lines can never cross.

## Conceptual questions

Compare and contrast the Coulomb force field and the electric field. To do this, make a list of five properties for the Coulomb force field analogous to the five properties listed for electric field lines. Compare each item in your list of Coulomb force field properties with those of the electric field—are they the same or different? (For example, electric field lines cannot cross. Is the same true for Coulomb field lines?)

[link] shows an electric field extending over three regions, labeled I, II, and III. Answer the following questions. (a) Are there any isolated charges? If so, in what region and what are their signs? (b) Where is the field strongest? (c) Where is it weakest? (d) Where is the field the most uniform?

## Problem exercises

(a) Sketch the electric field lines near a point charge $+q$ . (b) Do the same for a point charge $–3.00q$ .

Sketch the electric field lines a long distance from the charge distributions shown in [link] (a) and (b)

[link] shows the electric field lines near two charges ${q}_{1}$ and ${q}_{2}$ . What is the ratio of their magnitudes? (b) Sketch the electric field lines a long distance from the charges shown in the figure.

Sketch the electric field lines in the vicinity of two opposite charges, where the negative charge is three times greater in magnitude than the positive. (See [link] for a similar situation).

Determine the total force and the absolute pressure on the bottom of a swimming pool 28.0m by 8.5m whose uniform depth is 1 .8m.
for the answer to complete, the units need specified why
That's just how the AP grades. Otherwise, you could be talking about m/s when the answer requires m/s^2. They need to know what you are referring to.
Kyle
Suppose a speck of dust in an electrostatic precipitator has 1.0000×1012 protons in it and has a net charge of –5.00 nC (a very large charge for a small speck). How many electrons does it have?
how would I work this problem
Alexia
how can you have not an integer number of protons? If, on the other hand it supposed to be 1e12, then 1.6e-19C/proton • 1e12 protons=1.6e-7 C is the charge of the protons in the speck, so the difference between this and 5e-9C is made up by electrons
Igor
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angular velocity can be defined as the rate of change in radian over seconds.
Fidelis
Why does earth exert only a tiny downward pull?
hello
Islam
Why is light bright?
an 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit
thanks so much. i undersooth well
what is physics
is the study of matter in relation to energy
Kintu
physics can be defined as the natural science that deals with the study of motion through space,time along with its related concepts which are energy and force
Fidelis
a submersible pump is dropped a borehole and hits the level of water at the bottom of the borehole 5 seconds later.determine the level of water in the borehole
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power P = Work done per second W/ t. It means the more power, the stronger machine
Sphere
e.g. heart Uses 2 W per beat.
Rohit
A spherica, concave shaving mirror has a radius of curvature of 32 cm .what is the magnification of a persons face. when it is 12cm to the left of the vertex of the mirror
did you solve?
Shii
1.75cm
Ridwan
my name is Abu m.konnek I am a student of a electrical engineer and I want you to help me
Abu
the magnification k = f/(f-d) with focus f = R/2 =16 cm; d =12 cm k = 16/4 =4
Sphere
what do we call velocity
Kings
A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa
hi
Godfred
Godfred
If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
the same behavior thru the prism out or in water bud abbot
Ju
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
Anurag