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Learning objectives

By the end of this section, you will be able to:

  • Calculate the total force (magnitude and direction) exerted on a test charge from more than one charge.
  • Describe an electric field diagram of a positive point charge and of a negative point charge with twice the magnitude of the positive charge.
  • Draw the electric field lines between two points of the same charge and between two points of opposite charge.

The information presented in this section supports the following AP® learning objectives and science practices:

  • 2.C.1.2 The student is able to calculate any one of the variables – electric force, electric charge, and electric field – at a point given the values and sign or direction of the other two quantities.
  • 2.C.2.1 The student is able to qualitatively and semiquantitatively apply the vector relationship between the electric field and the net electric charge creating that field.
  • 2.C.4.1 The student is able to distinguish the characteristics that differ between monopole fields (gravitational field of spherical mass and electrical field due to single point charge) and dipole fields (electric dipole field and magnetic field) and make claims about the spatial behavior of the fields using qualitative or semiquantitative arguments based on vector addition of fields due to each point source, including identifying the locations and signs of sources from a vector diagram of the field. (S.P. 2.2, 6.4, 7.2)
  • 2.C.4.2 The student is able to apply mathematical routines to determine the magnitude and direction of the electric field at specified points in the vicinity of a small set (2-4) of point charges, and express the results in terms of magnitude and direction of the field in a visual representation by drawing field vectors of appropriate length and direction at the specified points. (S.P. 1.4, 2.2)
  • 3.C.2.3 The student is able to use mathematics to describe the electric force that results from the interaction of several separated point charges (generally 2-4 point charges, though more are permitted in situations of high symmetry). (S.P. 2.2)

Drawings using lines to represent electric fields around charged objects are very useful in visualizing field strength and direction. Since the electric field has both magnitude and direction, it is a vector. Like all vectors , the electric field can be represented by an arrow that has length proportional to its magnitude and that points in the correct direction. (We have used arrows extensively to represent force vectors, for example.)

[link] shows two pictorial representations of the same electric field created by a positive point charge Q size 12{Q} {} . [link] (b) shows the standard representation using continuous lines. [link] (b) shows numerous individual arrows with each arrow representing the force on a test charge q size 12{q} {} . Field lines are essentially a map of infinitesimal force vectors.

In part a, electric field lines emanating from the charge Q are shown by the vector arrows pointing outward in every direction of two dimensional space. In part b, electric field lines emanating from the charge Q are shown by the vector arrows pointing outward in every direction of two dimensional space.
Two equivalent representations of the electric field due to a positive charge Q size 12{Q} {} . (a) Arrows representing the electric field's magnitude and direction. (b) In the standard representation, the arrows are replaced by continuous field lines having the same direction at any point as the electric field. The closeness of the lines is directly related to the strength of the electric field. A test charge placed anywhere will feel a force in the direction of the field line; this force will have a strength proportional to the density of the lines (being greater near the charge, for example).

Questions & Answers

how vapour pressure of a liquid lost through convection
Yomzi Reply
Roofs are sometimes pushed off vertically during a tropical cyclone, and buildings sometimes explode outward when hit by a tornado. Use Bernoulli’s principle to explain these phenomena.
Aliraza Reply
Plz answer the question ☝️☝️
what's the basic si unit of acceleration
Explain why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.
Fabian Reply
Insulators (nonmetals) have a higher BE than metals, and it is more difficult for photons to eject electrons from insulators. Discuss how this relates to the free charges in metals that make them good conductors.
Muhammad Reply
Is the photoelectric effect a direct consequence of the wave character of EM radiation or of the particle character of EM radiation? Explain briefly.
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.
Henny Reply
how solve this problem?
P(pressure)=density ×depth×acceleration due to gravity Force =P×Area(28.0x8.5)
for the answer to complete, the units need specified why
muqaddas Reply
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.
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?
Alexia Reply
how would I work this problem
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
what is angular velocity
Obaapa Reply
angular velocity can be defined as the rate of change in radian over seconds.
Why does earth exert only a tiny downward pull?
Mya Reply
Why is light bright?
Abraham Reply
what is radioactive element
Attah Reply
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
Aisha Reply
thanks so much. i undersooth well
Valdes Reply
what is physics
Nwafor Reply
is the study of matter in relation to energy
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
Practice Key Terms 4

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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