# Electric field

### Electric field

#### Lessons

In this lesson, we will learn:
• Meaning of electric field and its relationship to electric force
• How to draw electric field line diagrams
• Solving problems with electric field
Notes:

• Electric field (E) is the electric force exerted by a charge Q on another charge q, per unit charge of q. It is a vector quantity.
• By convention, the direction of electric field vectors is defined as the direction that a positive test charge would move if placed in the field. Fe points in the same direction as E for positive charges, and in the opposite direction of E for negative charges.
• A test charge is a point charge with a very small magnitude. Test charges have a small magnitude charge so that the electric field of the test charge is negligible and does not affect the electric field that is being investigated.

Electric Field

$E= \frac{F_e}{Q}$
or equivalently, by substituting Coulomb's law:
$|E| = k \frac{|Q|}{r^2}$
$E:$ electric field, in newtons per coulomb (N/C)
$F_e:$ electric force, in newtons (N)
$q:$ charge that experiences the field, in coulombs (C)
$k:$ Coulomb's law constant, $9.00 \times 10^9 N\centerdot m^2 / C^2$
$|Q|:$ magnitude of charge that creates the field, in coulombs (C)
$r:$ distance from charge, in meters (m)

Coulomb's Law (Electric Force)

$|F_e| = k \frac{|Q_1 Q_2|}{r^2}$
$|F_e|:$ magnitude of electric force, in newtons (N)
$k:$ Coulomb's law constant, $9.00 \times 10^9 N\centerdot m^2 / C^2$
$|Q_1|, |Q_2|:$ magnitude of each charge, in coulombs (C)
$r:$ distance between charges, in meters (m)

• 1.
Calculations with electric field
A pair of positive and negative point charges are fixed in the following positions:
a)
Find the electric field (magnitude and direction) at point A.

b)
A charge placed at A experiences a force of $5.9 \times 10^{-3} N$ [right]. Find the magnitude and polarity of the charge.