Electromagnetic Induction — MHT-CET Physics

Formulas (1)

• Flux, Faraday's Law and Induced Charge · Faraday's law and induced charge
  $$e = -N\frac{d\phi}{dt}, \qquad q = \frac{N\,\Delta\phi}{R}$$

Reference tables (1)

Watch out for (3)

• Thinking a faster change moves more charge
  → Flux, Faraday's Law and Induced Charge
• Using the whole field for the flux
  → Flux, Faraday's Law and Induced Charge
• Opposing the flux instead of its change
  → Lenz's Law: the Induced Current Opposes the Change

Formulas (3)

• Motional e.m.f. Blv · Motional e.m.f.
  $$e = Blv$$
• Magnetic Braking: Force, Heat and Terminal Speed · Braking force and terminal speed
  $$F = \frac{B^2l^2v}{R}, \qquad v_t = \frac{mgR}{B^2l^2}$$
• Rotating Rods, Discs, Wheels and Coils · Rotating rod or disc
  $$e = \tfrac{1}{2}B\omega l^2$$

Watch out for (3)

• Using the total field instead of the cutting component
  → Motional e.m.f. Blv
• Forgetting that the braking force grows with speed
  → Magnetic Braking: Force, Heat and Terminal Speed
• Multiplying by the number of spokes
  → Rotating Rods, Discs, Wheels and Coils

Formulas (3)

• What Self-Inductance Is · Self-inductance
  $$N\phi = LI, \qquad e = -L\frac{dI}{dt}$$
• Self-Inductance of a Solenoid · Solenoid
  $$L = \frac{\mu_0 \mu_r N^2 A}{l} = \mu_0\mu_r n^2 A l$$
• Energy in an Inductor, and Inductors in Series and Parallel · Stored energy
  $$U = \tfrac{1}{2}LI^2$$

Watch out for (3)

• Forgetting the N in Nφ = LI
  → What Self-Inductance Is
• Holding N fixed when the question holds n fixed
  → Self-Inductance of a Solenoid
• Halving the energy when the current halves
  → Energy in an Inductor, and Inductors in Series and Parallel

Formulas (3)

• Mutual Inductance · Mutual inductance
  $$e_2 = M\frac{dI_1}{dt}, \qquad M_{\text{rings}} = \frac{\mu_0\pi r_2^2}{2r_1}$$
• Coefficient of Coupling · Coupling
  $$K = \frac{M}{\sqrt{L_1L_2}}$$
• Transformers and Generators · Transformer
  $$\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s}\ \text{(ideal)}$$

Watch out for (3)

• Putting the big ring's radius on top
  → Mutual Inductance
• Adding the inductances
  → Coefficient of Coupling
• Scaling current the same way as voltage
  → Transformers and Generators