Magnetism: Fields, Forces and Induction

Formulas (4)

• The magnetic field of a straight wire and of a solenoid · Field of a long straight wire and of a solenoid
  $$B_{\text{wire}} = \frac{\mu_0 I}{2\pi r} \qquad B_{\text{solenoid}} = \mu_0 \frac{N}{L} I$$
• The force on a current-carrying wire in a magnetic field · Force on a wire
  $$F = B I L \sin\theta$$
• The force on a moving charge: F = qvB sinθ · Force on a moving charge
  $$F = q v B \sin\theta$$
• Circular motion of a charged particle in a magnetic field · Radius and period of the circle
  $$r = \frac{m v}{q B} \qquad T = \frac{2\pi m}{q B}$$

Reference tables (1)

Watch out for (5)

• Attraction does not prove an object is a magnet
  → Magnets, poles, field lines and the Earth's field
• A wire's field falls as 1/r, not 1/r²
  → The magnetic field of a straight wire and of a solenoid
• No force when the current runs along the field
  → The force on a current-carrying wire in a magnetic field
• A magnetic field cannot change a particle's speed
  → The force on a moving charge: F = qvB sinθ
• Constant speed is not constant velocity
  → Circular motion of a charged particle in a magnetic field

Formulas (2)

• Magnetic flux and Faraday's law of induction · Faraday's law
  $$\Phi = B A \cos\theta \qquad \varepsilon = N \frac{\Delta \Phi}{\Delta t}$$
• Generators and transformers · Ideal transformer
  $$\frac{V_s}{V_p} = \frac{N_s}{N_p} \qquad V_p I_p = V_s I_s$$

Watch out for (5)

• A strong field alone induces nothing
  → Magnetic flux and Faraday's law of induction
• Thicker wire does not raise the induced e.m.f.
  → Magnetic flux and Faraday's law of induction
• The induced current opposes the change, not the field
  → Lenz's law: the direction of the induced current
• A transformer cannot increase power
  → Generators and transformers
• Transformers do not work on DC
  → Generators and transformers