# 18.5 Electric field lines: multiple charges  (Page 3/7)

 Page 3 / 7

We use electric field lines to visualize and analyze electric fields (the lines are a pictorial tool, not a physical entity in themselves). The properties of electric field lines for any charge distribution can be summarized as follows:

1. Field lines must begin on positive charges and terminate on negative charges, or at infinity in the hypothetical case of isolated charges.
2. The number of field lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.
3. 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.
4. The direction of the electric field is tangent to the field line at any point in space.
5. Field lines can never cross.

The last property means that the field is unique at any point. The field line represents the direction of the field; so if they crossed, the field would have two directions at that location (an impossibility if the field is unique).

## Phet explorations: charges and fields

Move point charges around on the playing field and then view the electric field, voltages, equipotential lines, and more. It's colorful, it's dynamic, it's free.

## 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).

#### Questions & Answers

What is specific heat capacity?
hamidat Reply
Specific heat capacity is the amount of heat required to raise the temperature of one (Kg) of a substance through one Kelvin
Paluutar
formula for measuring Joules
Rowshan Reply
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hamidat
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What limits the Magnification of an optical instrument?
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Lithography is 2 micron
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An hydraulic press is a type of machine that is operated by different pressure of water on pistons.
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Boyles law states that the volume of a fixed amount of a gas is inversely proportional to the pressure acting on in provided that the temperature is constant.that is V=k(1/p) or V=k/p
FADILAT
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Anderson
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the minimum thrust that an object must have in oder yo escape the gravitational pull
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Mua
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ADAMS
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Deena Reply
what are the laws of motion
Mua
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Ugwu Reply
Force is any quantity or a change that produces motion on an object body.
albert
A force is a push or a pull that has the tendency of changing a body's uniform state of rest or uniform state of motion in a straight line.
nicholas
plsoo give me the gravitational motion formulas
Okoye
f=Gm/d²
FADILAT
What is the meaning of emf
Chinedu Reply
electro magnetic force
shafiu
Electromotive force (emf) is a measurement of the energy that causes current to flow through a circuit.
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tritium (gas, netrogen, cloud, lamp)
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Continue - > tritium (gas, netrogen, cloud, lamp span, lamp light, cool)
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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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