{"id":67228,"date":"2026-09-07T06:38:20","date_gmt":"2026-09-06T21:38:20","guid":{"rendered":"https:\/\/phys-edu.net\/wp\/?p=67228"},"modified":"2026-09-07T06:38:20","modified_gmt":"2026-09-06T21:38:20","slug":"the-formula-fqe-what-it-reveals-about-electric-fields-unlocking-the-secret-of-lightning-rods","status":"publish","type":"post","link":"https:\/\/phys-edu.net\/wp\/?p=67228&lang=en","title":{"rendered":"The Formula “F=qE”: What It Reveals About Electric Fields \u2014 Unlocking the Secret of Lightning Rods"},"content":{"rendered":"

I’m Ken Kuwako, your Science Trainer. Every day is an experiment.<\/strong><\/span><\/p>\n

When teaching \u201cforce\u201d in science class, we often tell students that \u201cto exert a force on an object, you have to touch it.\u201d But electrostatic force<\/b> can act on objects from a distance, almost like a magnet, even when the objects are not touching. Familiar examples include hair standing on end after rubbing it with a plastic sheet, or the little \u201czap!\u201d you get from a doorknob on a dry winter day. These are all effects of this invisible force at work. Gravity is another fascinating force that can act on objects without any physical contact.<\/p>\n

To understand these forces that act without touching<\/b>, physics introduces the concept of a field<\/b>. We use the idea of a \u201cgravitational field\u201d for gravity and an electric field<\/b> for electrostatic force. These concepts allow us to make the invisible world of electricity more tangible and understand the nature of these forces more deeply.<\/p>\n

The concept of an electric field may seem a little abstract at first. But once you understand it, you can use the same idea to make sense of not only electrostatic forces, but also natural phenomena such as lightning and even everyday technologies such as lightning rods. So, let\u2019s explore the world of electric fields together and uncover some of the mysteries of electricity!<\/p>\n

\u25a02 The Formula for the Force Exerted by an Electric Field \u2014 Making the Invisible World of Electricity \u201cVisible\u201d<\/h3>\n

Let\u2019s start by looking at the formula that describes the force an electric field exerts on a charge.<\/span><\/p>\n

F<\/span>=<\/span><\/span>qE<\/span><\/span><\/span><\/span><\/span><\/div>\n

Force on a charge = Electric charge \u00d7<\/span><\/span><\/span><\/span><\/span> Electric field<\/b><\/p>\n

This simple formula is a powerful tool for understanding the invisible world of electricity.<\/p>\n

For example, suppose we have a charge A of +<\/span>1<\/span>C<\/span><\/span><\/span><\/span><\/span><\/b>. If we place a charged object with a charge of +<\/span>Q<\/span>[<\/span>C<\/span>]<\/span><\/span><\/span><\/span><\/span> nearby, charge A experiences an electrostatic force from the charged object. If the charged object were not there, charge A would not be affected. So, even though we cannot see it, we can think of the presence of the charged object as causing some kind of change in the surrounding space<\/b>.<\/p>\n

This \u201cchange in space\u201d is precisely what we describe using the concepts of the electric field<\/b> and electric potential<\/b>.<\/p>\n

Let\u2019s look at a specific example. Suppose we place charge A (+<\/span>1<\/span>C<\/span><\/span><\/span><\/span><\/span>) at a distance of 1<\/span> m<\/span><\/span><\/span><\/span><\/span><\/span> from a charged object with a charge of +<\/span>Q<\/span>[<\/span>C<\/span>]<\/span><\/span><\/span><\/span><\/span><\/b>. The electrostatic force FA acting on A is:<\/p>\n

FA =k Q\u00d71\/1^2 = kQ<\/p>\n

If, instead of charge A, we place a charge B of +<\/span>2<\/span>C<\/span><\/span><\/span><\/span><\/span> at the same location, the electrostatic force acting on B becomes F<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>2<\/span>k<\/span>Q<\/span>[<\/span>N<\/span>]<\/span><\/span><\/span><\/span><\/span>. If we express this F<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> using the force F<\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> acting on A, we get F<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>2<\/span>F<\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>. Likewise, if we place a charge D of +<\/span>3<\/span>C<\/span><\/span><\/span><\/span><\/span>, the electrostatic force acting on D<\/span><\/span><\/span><\/span><\/span> can be expressed as F<\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>3<\/span>F<\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>[<\/span>N<\/span>]<\/span><\/span><\/span><\/span><\/span>.<\/p>\n

In other words, if we know the force F<\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> experienced by a +<\/span>1<\/span>C<\/span><\/span><\/span><\/span><\/span> charge at a particular location, we can express the force experienced by other charges at that same location as multiples of F<\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>. So we use the +<\/span>1<\/span>C<\/span><\/span><\/span><\/span><\/span> charge as a reference<\/b> and define the force experienced by a +<\/span>1<\/span>C<\/span><\/span><\/span><\/span> charge<\/span><\/b> as the electric field E<\/span><\/span><\/span><\/span><\/span><\/b>. In the example above, F<\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> represents the electric field E<\/span><\/span><\/span><\/span><\/span>.<\/p>\n

Therefore, if a charge X with a charge of +<\/span>q<\/span>[<\/span>C<\/span>]<\/span><\/span><\/span><\/span><\/span> is placed in an electric field E<\/span><\/span><\/span><\/span><\/span>, the force F<\/span>X<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>qE<\/span><\/span><\/span><\/span><\/span> acting on X can be expressed as follows. The unit of electric field E<\/span><\/span><\/span><\/span><\/span> is N<\/span>\/<\/span>C<\/span><\/span><\/span><\/span><\/span><\/b> (newtons per coulomb).<\/p>\n

This idea of the electric field <\/span>E<\/span><\/span><\/span><\/span><\/span> is extremely useful. For example, imagine placing a <\/span>+<\/span>Q<\/span><\/span><\/span><\/span><\/span> charged object at various locations around a charge of <\/span>+<\/span>1<\/span>C<\/span><\/span><\/span><\/span><\/span> and measuring the electric field <\/span>E<\/span><\/span><\/span><\/span><\/span>. From the resulting distribution of the electric field, we can understand the \u201celectrical landscape\u201d created by the <\/span>+<\/span>Q<\/span><\/span><\/span><\/span><\/span> charge.<\/span><\/p>\n

The electric field is stronger closer to the charged object and becomes weaker as you move farther away. Even if you have no idea where the charged object itself is, you can determine the electric field by placing a <\/span>+<\/span>1<\/span>C<\/span><\/span><\/span><\/span><\/span> charge A at a particular location and measuring the force acting on it.<\/span><\/p>\n

In reality, electricity is invisible, so it is impossible to tell just by looking whether an object is charged or not. There could even be several charged objects hidden in different locations. Yet, even in such an \u201cunknown space,\u201d we can map out the distribution of the electric field by placing a +<\/span>1<\/span>C<\/span><\/span><\/span><\/span><\/span> charge A at different locations. This is very similar to measuring wind speed and direction at various places to understand weather conditions.<\/p>\n

Once we know the electric field at a particular location, we can calculate what kind of force a charge of a given size (<\/span>+<\/span>q<\/span>[<\/span>C<\/span>]<\/span><\/span><\/span><\/span><\/span>) will experience there and in which direction it will act, without knowing what created the field in the first place (from <\/span>F<\/span>=<\/span><\/span>qE<\/span><\/span><\/span><\/span><\/span>, simply multiply by <\/span>E<\/span><\/span><\/span><\/span><\/span>). Without the concept of an electric field, if all you knew was the formula for electrostatic force, you would have to find the other charge and measure the distance to it every single time. Now you can see just how powerful and useful the concept of an electric field really is.<\/span><\/p>\n

Electric Field and Electric Potential: Imagine an \u201cIncline\u201d in the World of Electricity<\/h3>\n

Next, let\u2019s look at another physical quantity that makes the world of electricity even easier to understand: <\/span>electric potential<\/b>. The electric field was the \u201cforce acting on a <\/span>+<\/span>1<\/span>C<\/span><\/span><\/span><\/span><\/span> charge.\u201d Put more simply, an electric field is a \u201cforce.\u201d So what is <\/span>electric potential<\/b>? You can think of it as \u201cheight\u201d in the world of electricity.<\/span><\/p>\n

For example, an object placed on a slope is pulled downhill by gravity and rolls along the slope. The steeper the slope, the greater the force acting on the object.<\/p>\n

We can picture an electric field in a similar way. Imagine a +<\/span>1<\/span>C<\/span><\/span><\/span><\/span><\/span> charge being acted upon by an electric field, as shown in the following diagram. We can introduce something corresponding to a new \u201cheight in electrical space\u201d<\/b> and imagine that the electric field is produced by the slope of this electrical landscape.<\/p>\n

\"\u30b9\u30af\u30ea\u30fc\u30f3\u30b7\u30e7\u30c3\u30c8<\/a><\/p>\n

\"\"<\/p>\n

This height is called electric potential<\/b> and is represented by V<\/span><\/span><\/span><\/span><\/span>. The \u201cslope\u201d created by the electric potential is what represents the electric field<\/b>. The stronger the electric field, the steeper the slope.<\/b><\/p>\n

For example, let\u2019s think about what the electric potential looks like around a charge of +<\/span>Q<\/span>[<\/span>C<\/span>]<\/span><\/span><\/span><\/span><\/span><\/b>. As shown on the left side of the following diagram, a strong electric field is produced near the charge Q<\/span><\/span><\/span><\/span><\/span>, while the field becomes weaker as you move farther away, spreading outward radially. The right side of the diagram represents the strength of this electric field using electric potential. Just as a stronger electric field corresponds to a steeper slope, the diagram shows a steeper slope near the charge Q<\/span><\/span><\/span><\/span><\/span>, becoming gentler with increasing distance.<\/p>\n

Compared with a diagram showing only the electric field, introducing electric potential as \u201cheight\u201d makes the electrical world much easier to visualize. So, using the ideas of electric field and electric potential, how can we visualize the way two positive charges repel each other, or a positive and a negative charge attract each other?<\/span><\/p>\n

Imagine holding a handkerchief horizontally and placing a marble on it. The marble stays still.<\/p>\n

If you pull the handkerchief upward<\/b> as shown in the following diagram, the marble rolls away from the place where the cloth is pulled upward. If you pull the handkerchief downward<\/b>, the marble rolls toward the lowered area. If we think of this \u201cpull\u201d as representing the electric potential created by positive or negative charges, and the marble as representing another positive charge, the forces acting between charges become much easier to understand intuitively.<\/p>\n

\"\"<\/p>\n

Image created using ChatGPT<\/p>\n

More precisely, electric potential is defined as the electrostatic potential energy (energy associated with \u201cheight\u201d) possessed by +<\/span>1<\/span>C<\/span><\/span><\/span><\/span><\/span> of electric charge. Its unit is [<\/span>J<\/span>\/<\/span>C<\/span>]<\/span><\/span><\/span><\/span><\/span><\/b> or [<\/span>V<\/span>]<\/span><\/span><\/span><\/span><\/span> (volts).<\/p>\n

\u30b0\u30ea\u30b0\u30ea\u52d5\u304b\u305b\u308b\uff01Geogebra\u3067\u96fb\u4f4d\u306e\u300c\u5c71\u3068\u8c37\u300d\u3092\u4f5c\u3063\u3066\u96fb\u5834\u3068\u96fb\u4f4d\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3088\u3046\uff01<\/a><\/p><\/blockquote>\n