Section 5.8: Problem-Solving Strategies

To solve magnetic field and induction problems effectively, follow a structured approach:

  • Identify known quantities: currents, velocities, charges, field strengths.
  • Draw clear diagrams showing forces, fields, and current directions.
  • Use relevant formulas: Lorentz force, Faraday’s law, self-inductance, energy stored.
  • Check dimensions and units carefully.
  • Break complex problems into simpler parts and solve step by step.

Example 1

A 0.5 m wire moves perpendicular to a 0.8 T magnetic field with speed 3 m/s. Find the induced EMF if the wire length is 0.5 m.

EMF: \( \mathcal{E} = B L v = 0.8 * 0.5 * 3 = 1.2 \text{ V} \)

Example 2

Calculate the energy stored in a 2 H inductor carrying 5 A current.

Energy: \( U = \frac{1}{2} L I^2 = 0.5 * 2 * 5^2 = 25 \text{ J} \)

Practice Problems

  1. A conductor of length 0.3 m moves at 4 m/s in a 0.6 T magnetic field. Find EMF induced.
  2. Energy stored in a 4 H inductor carrying 2.5 A current?
  3. Explain qualitatively how Lenz’s law ensures energy conservation.
  4. A circular coil has 10 turns and radius 0.2 m. Magnetic field changes from 0.5 T to 1.5 T in 0.2 s. Find average induced EMF.
  5. Sketch current vs time for an RL circuit when switch is closed.
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