Electromagnetic Induction

Question 1

Electro-Magnetic Equilibrium

Answer 1

• Direction of magnetic force F_B pushing electrons down or up a wire will leave an excess of positive charge on the opposite end
  
  • The separation of charge creates a uniform electric field E, within the wire pointing downward
    
    • A charge q in the wire feels two forces: an electric force (F_E= qE) and magnetic force (F_B= qvB)
      
      • If q is negative, F_E is upward and F_B is downward
      • If q is positive, F_E is downward and F_B is upward
        
        • In both cases, the forces act in opposite directions
        • Once the magnitude of F_E equals the magnitude of F_B the charges in the wire are in electro-magnetic equilibrium
          
          • Occurs when qE= qvB or (E= vb)
    • The presence of the electric field creates a potential difference between the ends of the wire
      • The potential difference V_ba= El_length (point b at upper end, point a lower end)
        
        • As E= vB, V_ba= vBl_length

Question 2

Motional EMF

Answer 2

• Given a Rod sliding along a pair of conducting rails connected at the left by a stationary bar, the sliding rod completes a rectangular circuit, with the potential difference V_ba causing current to flow
  
  • The motion of the sliding rod through the magnetic field creates an electromotive force called motional emf:
    
    • ℰ= vBl_length
      
      • Existence of a current in sliding rod causes the magnetic field to exert a force on it

Question 3

Power of External Agent on Rod

Answer 3

• Formula F_B= I_currentl_lengthB and the right-hand rule determine the direction of F_B on the rod (existence of current in sliding rod causes magnetic field to exert force on it)
  
  • An external agent must provide the same amount of force in the opposing direction to maintain the rod’s constant velocity and keep the current flowing
    
    • Power that external agent must supply is P= Fv= I_currentl_lengthBv
      
      • The electrical power delivered to the circuit is P= IV_ba= Iℰ= I_currentvBl_length
        
        • _​Two equations are identical
          
          • The energy provided by the external agent is transformed first into electrical energy and then into thermal energy as the conductors making up the circuit dissipate heat

Question 4

Magnetic Flux

Answer 4

• The magnetic flux, Φ_B, through an area A is equal to the product of A and the magnetic field perpendicular to it: Φ_B= B_perpA= BAcosθ
  
  • Magnetic flux measures the densit of magnetic field lines that cross through an area
    
    • The direction of A is taken to be perpendicular to the plane of the loop

Question 5

Faraday’s Law of Electromagnetic Induction

Answer 5

• The emf induced in a circuit is equal to the rate of change of the magnetic flux through the circuit
  
  • ℰ_avg= -ΔΦ_B/Δt
  • Induced emf can produce a current, which will make its own magnetic field
    
    • Direction of induced current is determined by the polarity of the induced emf and is given by Lenz’s law: The induced current will always flow in the direction that opposes the change in magnetic flux that produced it
      
      • Violation of Lenz’s law would lead directly to a violation of the law of conservation of energy
      • Flux is scalar and has no direction, but referring to the “direction” of flux makes applying Lenz’s law easier
        
        • What is actually referred to is the direction of the field producing the flux