Notes
Magnetic fields
- Magnetic field lines go from north to south outside a magnet. Magnetic poles always come in pairs (no isolated poles).
- Moving charges and currents create magnetic fields. Around a long straight wire: $\displaystyle B = \frac{\mu_0I}{2\pi r}$. Use the right-hand rule: thumb along the current, fingers curl in the direction of $\vec B$.
- Materials: ferromagnetic (iron) is strongly attracted; paramagnetic slightly; diamagnetic slightly repelled.
Magnetic force
- On a moving charge: $F = qvB\sin\theta$. The force is perpendicular to both $\vec v$ and $\vec B$, so it does no work and can't change the speed.
- A charge moving perpendicular to a uniform field moves in a circle: $\displaystyle qvB = \frac{mv^2}{r} \Rightarrow r = \frac{mv}{qB}$.
- On a current-carrying wire: $F = I\ell B\sin\theta$.
- Parallel wires with currents in the same direction attract; opposite directions repel.
Electromagnetic induction
- Magnetic flux: $\Phi_B = BA\cos\theta$.
- Faraday's law: a changing flux induces an emf: $\displaystyle \varepsilon = -N\frac{\Delta\Phi_B}{\Delta t}$.
- Lenz's law: the induced current creates a field that opposes the change in flux.
- A conducting rod moving through a field: $\varepsilon = B\ell v$.
- Uses: generators, transformers, induction cooktops, credit card readers.
Practice
$\sin 0° = 0$.
Perpendicular forces change only direction.
$F = qvB = (1.6 \times 10^{-19})(2.0 \times 10^6)(0.50)$.
Like currents attract.
$\displaystyle B \propto \frac{1}{r}$.
Lenz's law: the induced field opposes the increasing flux.
$\varepsilon = B\ell v = 0.20(0.50)(4.0)$.
Only a changing flux induces an emf.
Free response
Write your answer first, then open the scoring guide.
Free-response question
A square loop of wire with side 0.10 m and resistance 2.0 Ω is in a magnetic field perpendicular to the loop. The field increases uniformly from 0 to 0.80 T in 0.20 s.
(a) Find the induced emf.
Show the answer and scoring guide
$\Delta\Phi = (0.80)(0.010) = 0.0080$ Wb. $\displaystyle \varepsilon = \frac{0.0080}{0.20} = 0.040$ V.
Check off the points you earned:
(b) Find the induced current.
Show the answer and scoring guide
$\displaystyle I = \frac{0.040}{2.0} = 0.020$ A.
Check off the points you earned:
(c) The field points out of the page. State the direction of the induced current and explain.
Show the answer and scoring guide
Clockwise (viewed with the field pointing toward you). The flux out of the page is increasing, so the induced current makes a field into the page inside the loop, which is clockwise by the right-hand rule.
Check off the points you earned: