practice questions

• Electromagnetic induction


  The generation of current due to relative motion between a wire and a magnetic field
• Faraday's law


  A changing magnetic field through a coil induces a current in it
• Faraday's law of induction


  A potential difference is induced in a loop when there is a change in the magnetic flux through the loop
• Electromagnetic induction


  1. Changing magnetic field

  2. Induced current in loop
• The current induced in a loop by a changing magnetic field produces a magnetic field that opposes this change in magnetic field
• Magnetic flux is the product of the average magnetic field and the area perpendicular to it that it penetrates
• Gauss's law for magnetic fields states that the magnetic field lines must form closed loops and there exist no magnetic monopoles
• Decreasing magnetic field


  Induces a current in a loop
• Rotating a loop about an axis parallel to the magnetic field

  Induces a current in the loop
• Moving a loop within a magnetic field


  Induces a current in the loop
• A changing magnetic field induces an electric field
• The magnitude of the induced emf in a loop is proportional to the rate of change of magnetic flux through the loop
• A steady current in a straight wire will not induce a current in a nearby stationary loop
• Decreasing the current in a straight wire

  Induces a current in a nearby loop
• Moving a loop parallel to a straight wire with constant current

  Does not induce a current in the loop
• Rotating a loop about a point next to a straight wire with constant current


  Does not induce a current in the loop
• Decreasing the current in a straight wire

  Induces a counterclockwise current in a nearby loop
• Moving a loop perpendicular to a straight wire with constant current


  Induces a clockwise current in the loop, proportional to the current in the wire
• Moving a loop parallel to a straight wire with constant current

  Induces no current in the loop
• Decreasing current in a straight wire

  Induces a loop to be attracted to the wire with a counterclockwise induced current
• The equation ∮ E⃗ .ds = - dϕB/dt indicates that changing magnetic flux induces an electric field
• Units for inductance


  • H (Henry)
  • J/A^2
  • Tm^2/A
• Primary energy storage form of an inductor

  Magnetic field
• What an inductor opposes


  Changes in current
• Energy stored

  When 50 A flows through a 20 H inductor
• Current changing more rapidly

  • Current I1
  • Current I2
  • Both are constant
  • Both are changing at the same rate
• Inductor with time-dependent current

  Magnitude of the emf induced by the inductor at time t = 0.3 s
• Current flowing through 1.2 H inductance

  So that the energy stored is 393 J
• Energy stored in inductor initially is U

  Energy stored in inductor if current is doubled and inductance is halved
• Energy stored in inductor

  • U/2
  • U
  • 2U
  • 4U
• Potential difference ΔVL across 10 mH inductor

  Maximum magnitude over the period shown
• Initial current i0 when switch S1 is just closed

  In RL circuit with 9 V battery, 50 Ω resistor, 10 H inductance
• Final steady state current if

  In RL circuit with 9 V battery, 50 Ω resistor, 10 H inductance, switch closed for t > 5τ
• Final steady state current if

  • 0 A
  • (9/50) A
  • (9/60) A
  • (50/9) A
• Inductive time constant


  For RL circuit
• Initial current through circuit


  Immediately after switch is closed in parallel RL circuit
• Currents through R1, R2, L1


  After switch is closed for a long time in parallel RL circuit
• Initial current through circuit


  Immediately after switch is closed in parallel RLC circuit
• What happens when switch is closed


  In RL circuit with battery, inductor, resistor
• What happens


  • No current will flow
  • Current will rise slowly to I = V/R
  • Current will gradually rise to I = V/R in the direction shown
  • Current will start at I = V/R in the direction shown and then drop to zero