Electric Forces and Fields

Question 1

Electric Charge

Answer 1

• The electromagnetic force holds atoms together
• Protons and electrons have intrinsic quality called electric charge that gives them an attractive force
  
  • Charge is conserved, net charge cannot be created or destroyed (E.G. negative charge gained equal to positive charge left)

Question 2

Elementary Charge

Answer 2

The magnitude of charge on an electron (and therefore on a proton) is denoted e, which stands for elementary charge as it is the basic unit of electric charge

• The charge of an ionized atom must be a whole number times e because charge can be added or subtracted only in packets of size e (quantized)

Question 3

Coulomb

Answer 3

• The charge of a particle (or object) is denoted by the letter q
  
  • In the SI system of units, charge is expressed in coulombs (abbreviated C)
    
    • One coulomb is a tremendous amount of charge: the value of e is about 1.6 x 10^-19 C

Question 4

Coulomb’s Law

Answer 4

• The electric force between two charged particles obeys the same mathematical law as the gravitational force between two masses (inverse-square law)
  
  • The electric force between two particles with charges of q₁ and q₂, separated by a distance r, is given by the equation:
    
    • |F_E|= k|q₁ + q₂|/r² (Coulomb’s Law)
      
      • Absolute value symbol is needed to give the magnitude of the force
      • The value of the proportionality constant, k, depends on the material between the charged particles
        
        • In empty space (vacuum)- or air, it is called Coulomb’s constant and has the value k= 9 x 10⁹ N x m²/C²
          
          • The relative sizes of the universal gravitational constant, G (6.7 x 10^-11 N x m²/kg²) and Coulomb’s constant shows the relative strengths of the electric and gravitational fields: The value of k is orders of magnitude larger than G

Question 5

Superposition

Answer 5

Consider three point charges: q₁, q₂, and q₃

• The total electric force acting on, q₂ for example is simply the sum of F_1-on-2 (the electric force on q₂ due to q₁) and F_3-on-2
  
  • F_{on 2}= F_1-on-2 + F_3-on-2
• The fact that electric forces can be added in this way is known as superposition

Question 6

The Electric Field

Answer 6

• The presence of a charge creates an electric field in the space that surrounds it
  
  • Another charge placed in the electric field created by the first charge will experience a force due to the field
• Intrinsic strength of the field is due to the source charge, independent of whatever test charge used to measure it
• Given point charge Q in a fixed position, test charge q (test charge is always assigened to be positive in electrostatics) is moved various locations near Q, and at each location the force the test charge experienced is measured, F_{on q}, divide the force by the test charge q to get the resulting vector, the electric field vector E at that location
  
  • E= F_{on q}/ q
    
    • Divide by test charge, as E vector is independent of strength of charge, ratio of test charge strength and its Force would be cancel out if divided
• If source charge is positive, the electric field vectors point away from it
• If source charge is negative, then the field vectors point towards it
  
  • Force decreases as test charge gets further from the source charge (1/r²) so the electric field vectors farther from the source charge are shorter than those that are closer
• Electric field always perpendicular to the surface

Question 7

Strength of Electric Field

Answer 7

• The force on the test charge q has a strength of kqQ/r² (Coloumb’s law), divide by q to determine intrinsic strength of the electric field created by the point charge source of magnitude Q
  
  • E= kQ/r²
• To make sketching electric fields easier, lines are drawn through the vector such that the electric field vector is tangent to the line everywhere it’s drawn
  
  • Where the field lines are denser, the field is stronger

Question 8

Adding Electric Fields

Answer 8

• Electric field vectors can be added like any other vectors
  
  • Given two source chrages, their fields would overlap and effectively add
    
    • A third test charge would feel the affect of the combined field
    • E_total= E₁ + E₂ (superposition)
    • Electric field lines always point away from positive source charges and toward negative ones
      
      • A charge feeling a force due to an existing E will want to move in the direction of E if it is positive and opposite if it’s negative
• Two equal but opposite charges form a pair called an electric dipole
  
  • If a positive charge q+ was placed in an electric dipole, it would experience a force that is tangent to, and in the same direction as the field line passing through +q’s location
  • If a negative charge -q was placed in an electric dipole it would experience a force that is tangent to, but in the direction opposite from the field line passing through -q’s location
• Electric field lines never cross

Question 9

Conductor and Insulator

Answer 9

Conductor: Materials that permit the flow of excess charge are called conductors, they conduct electricity

• Metals are excellent conductors due to their mobilized electrons
• There can be no electric field within the body of a conductor
  
  • ​Excess electrons that are deposited on a conductor move quickly to the surface, any excess charge on a conductor resides entirely on the outer surface
    
    • Can shield from electric fields by surrounding by metal (E.G. tunnel is surrounded by metal, within tunnels singals (electromagnetic waves) can’t penetrate and reception is lost)

Insulators: Materials with rigid electrons unable to roam throughout its atomic lattice

• E.G. glass, wood, rubber, and plastic
• Excess charge placed on an insulator stays put

Question 10

Semiconductor and Superconductor

Answer 10

Midway between conductors and insulators is a class of materials known as semiconductors (E.G. silicon)

Superconductors are exreme examples of conductors, offering absolutely no resistance to the flow of charge

• Perfect conductor of electric charge
• Many metals and ceramics become superconducting when they are brought to extremely low temperatures