
A force field diagram is a tool for visualizing the electric forces around charged objects. The electric field is a vector that represents the force on a positive test charge. By convention, the electric field points in the direction of the electrostatic force on a positive test charge. Because of this, electric field lines point away from positive source charges and toward negative ones. The strength of the electric field (in newtons per coulomb, or N/C) is the force felt by a charged particle divided by the particle’s electric charge. The closer the field lines are to each other, the stronger is the force.

electric field, electric field lines


$${F}_{e}=qE\text{or}E=\frac{{F}_{e}}{q}$$

 $$E=\frac{{k}_{e}q}{{r}^{2}}$$



Review problems and questions 

 An atom consists of a positively charged nucleus surrounded by one or more negatively charged electrons, which occupy a region of space known as the electron cloud.
 Which of the diagrams depicts the electric field generated by the nucleus?
 Which diagram correctly shows the directions of electric forces on the electrons?
 Did you choose the same diagram for the previous two questions? Why or why not?

 Diagram (i) correctly depicts the electric field surrounding the nucleus. This is because electric field lines always point away from a positive charge, and they always represent the net electrostatic force upon an imaginary positive test charge.
 Diagram (ii) correctly depicts the directions of the forces that the nucleus exerts upon electrons. That’s because electrons are negatively charged, and they are attracted to the positive nucleus.
 No. The net electrostatic force upon a negatively charged particle will always be in the direction opposite to the electric field vectors.


A commonly encountered unit of charge in consumer electronics is the milliamphour, or mAh, and in the USA the pound, or lb, is a commonly used unit of force. How many newtons per coulomb (N/C) would be equivalent to 1 lb/mAh?

1 lb/mAh = 1.2 N/C. You can work out the conversion factor as follows:$$\begin{array}{c}1\text{mA}=\frac{1\text{A}}{\mathrm{1,000}}=0.001\text{A}\\ 1\text{A}=\frac{1\text{C}}{\text{s}}\\ 1\text{mA}=\frac{0.001\text{C}}{\text{s}}\\ 1\text{hr}=60\mathrm{min}\times \frac{60\text{s}}{\mathrm{min}}=3,600\text{s}\\ 1\text{mAh=}\frac{0.001\text{C}}{\text{s}}\times 3,600\text{s}=3.6\text{C}\\ \text{1lb=4}\text{.4N}\\ \text{1}\frac{\text{lb}}{\text{mAh}}=\frac{4.4\text{N}}{3.6\text{C}}=1.2\frac{\text{N}}{\text{C}}\end{array}$$

 Rebecca inflates a rubber party balloon, ties it to a string, and hangs it from the ceiling. Then she rubs the balloon with a wool sweater. Suppose that she transfers one trillion “extra” electrons (10^{12} e^{−}) to the balloon. Assume, too, that you can pretend that all of this excess charge is located at the center of the balloon. What is the electric field strength 1 m from the center of the balloon?

Answer: The field strength is −1,440 N/C.
Asked: electric field strength E Given: number of excess electrons = 10^{12}; distance from charge, r = 1 m Relationship: electric field around a point charge, E = k_{e}q/r^{2} Solution: The solution requires us to multiply the number of electrons by the charge on one electron to obtain the total net charge of the balloon:$$\begin{array}{c}E=\frac{{k}_{e}q}{{r}^{2}}\\ E=\frac{\left(9.0\times {10}^{9}\frac{{\text{Nm}}^{\text{2}}}{{\text{C}}^{\text{2}}}\right)\left({10}^{12}{\text{e}}^{}\right)\left(1.6\times {10}^{19}\frac{\text{C}}{{\text{e}}^{}}\right)}{{\left(1\text{m}\right)}^{2}}\\ E=1,440\frac{\text{N}}{\text{C}}\end{array}$$The minus sign indicates that a positive test charge lying outside of the balloon would be drawn toward the balloon and therefore that the electric field points inward toward the balloon. Keep in mind that, while a trillion sounds like a lot of electrons, it only adds up to a negative charge of 1.6×10^{−7} C, or 160 billionths of a coulomb; and onetrillion electrons could be taken from just 1.7 trillionths of one mole of hydrogen atoms.

 Declare each of the following statements as true or false, based upon the accompanying electric field diagram.
 Object A is positively charged.
 Objects A and B have opposite charges.
 The electric field at point x is stronger than that at point y.

 True. Electric field lines, by convention, point away from positive charges.
 False. The field lines also point away from Object B, indicating that it is positive. Notice also that the field lines from Object A seem to push against those from Object B, and this is what happens when two like charges are brought close together.
 False. The closer field lines are to one another, the stronger the electric field is.

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