Question

What is an electric field? How do you determine the magnitude and direction of the field at a given point?

Answer 1

What is an electric field?

Electric field is a region of space in which a charged particle is under the influence of electric force.

How do you determine the magnitude and direction of the field at a given point?

Electric field is a vector quantity because an electric field has both magnitude and direction. The electric field experience by a charged particle is represented by electric field lines of force. Electric field lines of force start on positive charges and terminating on negative charges. The electric field around an isolated positive charge is drawn radially outward, because positive charges repel each other. Therefore, the field lines point away from a positive charge and towards a negative charge. The direction of the force on a positive charge is chosen arbitrarily as the direction of the electric field.

The magnitude and direction of the electric field are expressed by the value of
`\overline{E}`, called electric field strength or electric field intensity or simply the electric field.

From Coulomb's law, electric charge q₁ at position x₁ exerts a force on a particle with charge q₀ at position x₀

`\overline{F} = k(q_(1)q_(o))/(r^(2))a_(1,0)`

The electric field strength,
`\overline{E}`, at a point x₀ may be defined as the electric force
`\overline{F}` exerted per unit positive electric charge q₁ at that point.

⇒
`\overline{E} = \frac{\overline{F}}{q_(o)}a_(1,0)`

The electric field strength is;

`\overline{E} = k(q_(1))/(r^(2))a_(1,0)` (N/C or volts/m)

where

Electric constant k = 1/4πε₀

q₁ and q₀ are electric charges

`a_(1,0)` is the unit vector in the direction from point x₁ to point x₀

r is the distance between x₁ and x₀ of the point charges q₁ and q₀ respectively