22.8:
Electric Field
Consider a test charge in the vicinity of many source charges: q–i, where i ranges from 1 to N. The principle of superposition of Coulomb forces implies that the force on Q is the vector sum of the forces due to each q. This expression can be rearranged to express the force as Q times a vector quantity, called the electric field.
If the test charge were different, the electric field would not change. Thus, it helps formulate the effect of source charges independent of the test charge.
By definition, it follows the principle of superposition. At any point, the electric fields of the source charges are vectorially added to give the net electric field.
The direction of the electric field is chosen to be the direction of the force that a positive test charge would experience. Hence, a negative test charge would experience a force opposite to the field’s direction.
Thus, the electric field of a positive point charge is directed away from it, and a negative point charge is directed towards it.
22.8:
Electric Field
Consider two point charges, each exerting Coulomb force on the other. It is possible to describe the Coulomb interaction via an intermediate step by defining a new physical quantity called the electric field.
In the new picture, imagine that the first charge sets up an electric field independent of all other charges in the universe. When another charge comes in its vicinity, the second charge experiences an electric force depending on the electric field at that point. The source charge does not exert any force on itself; however, all the other charges exert force on it.
The SI unit of the electric field is newton per coulomb. Since the electric field is a vector quantity, it is called a vector field. Since the Coulomb interaction follows the principle of superposition, by definition, so does the electric field.
It is to be noted that the electric field is defined by considering the test charge as a point charge. If the charge had a significant spatial extent, its different parts would experience different forces. In reality, since charges are quantized, and the fundamental unit is the charge of an electron or a proton, which are practically point charges, this is a good approximation.
The electric field is defined along the direction of the Coulomb force a positive charge would experience. Since a positive source charge would repel this positive test charge, the electric field of the positive point charge is directed away from it. On the other hand, the positive test charge would be attracted by a negative source charge; hence the electric field of the negative point charge is directed into it.
Suggested Reading
- Young, H.D and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson; section 21.4; page 698.
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from https://openstax.org/details/books/university-physics-volume-2; section 5.4; page 198.