Force and Electric Fields Elliott

Coulomb’s Law There are many parallels between gravity fields and electric fields.   The electric field is the region of force around a point charge.

In 1784 Charles Augustine de Coulomb showed that the force between two point charges was proportional to each charge and inversely proportional to the square of the distance between them.  (Newtons Law of Gravitation is very similar).

The constant k has a value of 8 The constant k has a value of 8.99 ´ 109 Nm2 C-2 for two charges in a vacuum.  The constant is not normally written as k, but instead: This term e0 (‘epsilon nought’ - e is a Greek letter ‘e’) is called the permittivity of free space.  

Task Use the equation to calculate the force of two like charges and two unlike charges (make up any numbers you want). Compare and explain the forces produced.

Point of Note: The force F is positive when the charges are both positive or both negative; this indicates that the force is repulsive, which is borne out by our elementary observations of electrostatics.  If one charge is positive and the other is negative, we can easily see that the force F is negative, therefore attractive.

Check Your progress Describe the similarities and differences between the forces in a gravity field and electric field. Find the electrostatic force between a proton and an electron in a hydrogen atom if their separation is 5.3 ´ 10-11 m.  What does the sign tell you?

Answers 4pe0 r2 F = 9 ´ 109 m/F ´ +1.6 ´ 10-19 C ´ -1.6 ´ 10-19 C 1) The "shape" of the formula is the same  i.e. F = k × quantity 1 × quantity 2                                                                                                   r2  The constant is much bigger in an electric field.   The electric field can be both repulsive and attractive, whereas gravity is never repulsive 2) Formula first: F =  __1__ Q1Q2                                    4pe0      r2 F = 9 ´ 109 m/F ´ +1.6 ´ 10-19 C  ´ -1.6 ´ 10-19 C                            (5.3 ´ 10-11 m)2 F = - 8.20 ´ 10-8 N The minus sign tells us that the forces are attractive.

Electric Forces as Vectors While gravity fields and forces are attractive, electric forces and fields can be repulsive or attractive.  Force and field are both vector quantities in both situations. 

Resultant Forces Charges in Line If we place a point charge between two other charges we can consider three different situations.

Charges Not in Line

Electric Field Strength A gravity field is where a force is exerted on a mass; an electric field is a region where a force is exerted on a charge.   The electric field strength is defined as force per unit charge.   In equation form this is represented as: E = F/Q     [E – electric field strength; F – force; Q – charge] E is a vector quantity and its units are newtons per coulomb, N/C.  It can be negative (attractive) or positive (repulsive).

Check Your Progress

Answer

Formula Since the electric field strength is defined as force per unit charge, we can write: This equation is true for all point charges, which can be considered to have a radial field.

Point and Spherical Charges A spherical charge can also be considered to have a radial field provided the distance from the charge to the centre is much greater than the radius of the sphere.

Check Your Progress From the diagram how can you tell the value of the electric field strength? A charge of +1.6 ´ 10-19 C has a force of 8.7 ´ 10-15 N exerted on it when it is placed a certain point in a radial electric field.  What is the electric field strength?

Answer 1) The closer the field lines are together... ...the stronger the field. 2) E = F/Q = 8.7 ´ 10-15 N ¸ +1.6 ´ 10-19 C E = 5.4 ´ 104 N/C