State that the direction of an electric field at a point is the direction of the force on a positive charge at that point

4.2.1 Electric Charge

Key Concepts

Electric charge is a fundamental property of matter. Objects can have a net positive charge, a net negative charge, or be electrically neutral.

• Charge is quantised – it occurs in integer multiples of the elementary charge \$e = 1.602 \times 10^{-19}\,\text{C}\$.
• Like charges repel; unlike charges attract.
• Charge is conserved – the total charge in an isolated system remains constant.

Units and Symbols

The SI unit of charge is the coulomb (C). The symbol for charge is \$q\$ (or \$Q\$ for a total charge).

Electric Field

An electric field \$\mathbf{E}\$ exists in the region around a charged object. It is a vector quantity that describes the force that would be experienced by a test charge placed at any point in the field.

Definition of direction: The direction of the electric field at a point is defined as the direction of the force that would act on a positive test charge placed at that point.

Mathematically, the electric field is given by

\$\mathbf{E} = \frac{\mathbf{F}}{q_{\text{test}}}\$

where \$\mathbf{F}\$ is the force on the test charge \$q_{\text{test}}\$ (taken as positive).

Implications of the Definition

1. If the test charge is positive, the force direction is the same as the field direction.
2. If the test charge is negative, the force direction is opposite to the field direction.
3. Field lines are drawn:

   • Leaving positive charges.
   • Entering negative charges.
   • Never crossing each other.

Example

Consider a point charge \$+5\,\mu\text{C}\$ at the origin. At a point \$P\$ located \$0.10\,\text{m}\$ to the right of the charge, the electric field points to the right because a positive test charge placed at \$P\$ would be repelled away from the source charge.

Summary

• The direction of an electric field at any point is the direction of the force on a positive test charge at that point.
• This definition allows us to visualise electric fields using field lines and to predict the motion of charges in the field.