Electrostatic Force and Electric Fields – Learn

Electric field strength allows us to quantitatively look at electric fields. Mathematically, the electric field, , is given by:

where;

= the electric field strength in

= the force on the charged particle in

= the charge on the object experiencing the force in

The previous equation is also commonly arranged to give:

The acceleration of a charged particle in an electric field can also be determined by using Newton’s 2nd Law:

where;

= the acceleration of the charged particle in

= the mass of the accelerating particle in

Coulomb’s Law

Coulomb’s Law is used to determine the force between two charged particles:

where:

= the force on each charged object (in N)

and = the charges on the two points (in C)

= the distance between each charged point (in m)

= the permittivity of free space, which is equal to 8.854 × 10−12 A2S4Kg−1m−3 in air or in a vacuum.

is known as Coulomb’s constant, k, and is equal to 8.9875 × 10Nm2C−2. This is usually rounded off to 9.0 × 10Nm2C−2 for calculations.

Coulomb’s Law can now become:

where k = 9.0 × 10Nm2C−2

Example 1:

Calculate the uniform electric field that will cause a force of 2.4 × 1022 N on an electron (qe = −1.602 × 1019 C)

using:

, or

in the opposite direction to the force

Example 2:

Calculate the acceleration of the electron in example 1 (mass of an electron = 9.1 × 1031 Kg):

using:

and rearranging to give:

Example 3:

Calculate the force between 2 protons that are separated by 5mm (qp = 1.602 × 10−19 C):