U of T · Introduction to Physics II · Winter

PHY132H1: fields, light, and relativity.

The second half: electricity and magnetism, which turn out to be one thing; light, which turns out to be a consequence of them; and special relativity, which follows from taking the speed of light seriously.

About this course

Where the fundamental forces appear.

PHY132H1 "Introduction to Physics II" covers electricity, magnetism, light, optics and special relativity. Like PHY131H1 it runs 36 lecture hours and 20 practical hours with a lab kit fee of about 53 dollars. The prerequisite is PHY131H1, and calculus is a recommended co-requisite — MAT159H1 qualifies.

What changes from PHY131H1. Mechanics dealt with contact and gravity, both intuitive. Here the central object is a field: an influence filling space, which acts on anything placed in it. Nothing touches anything, and getting comfortable with that is most of the difficulty.

01

Chapters

In course order. Each page has the concept, worked examples, the diagram habits that make problems tractable, pitfalls, and practice.

PHY132H1Physics II · Winter PHY131H1prerequisite Co-reqcalculus recommended
  1. Electric charge & force

    Coulomb's law and the superposition of forces.

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  2. The electric field

    Fields, field lines, and Gauss's law.

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  3. Electric potential

    Potential energy, voltage, and capacitance.

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  4. Current & circuits

    Ohm's law, resistance, and Kirchhoff's rules.

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  5. Magnetic fields

    Forces on charges and currents; sources of the field.

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  6. Induction

    Faraday's law, Lenz's law, and where electricity comes from.

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  7. Electromagnetic waves & light

    Maxwell's synthesis and the nature of light.

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  8. Geometric optics

    Reflection, refraction, mirrors and lenses.

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  9. Wave optics

    Interference, diffraction, and why light is a wave.

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  10. Special relativity

    Time dilation, length contraction, and $E = mc^2$.

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02

Textbook Spine

The calendar lists the topics in the order used here. This guide follows the standard introductory sequence — electrostatics, circuits, magnetism, then light — which every major first-year text shares. Check the syllabus on Quercus for the assigned text, edition and problem numbers.

Unit-to-topic alignment
Electricity at rest

Units 1-3 cover the calendar's "electricity": charge, force, field and potential. The pattern to notice is that force relates to field exactly as potential energy relates to potential.

Electricity in motion

Unit 4 covers circuits, where the abstractions of Units 1-3 become measurable quantities. This is the most immediately practical material in the course.

Magnetism

Units 5-6 cover "magnetism". The theme is that magnetism is what electricity looks like when charges move, and that changing one field creates the other.

Light and relativity

Units 7-10 cover "light, optics, special relativity". Light emerges from the field equations, behaves as a ray in Unit 8 and a wave in Unit 9, and its constant speed forces relativity in Unit 10.

DRAW

Sketch the field

Field lines before equations. Direction errors dominate this course, and a sketch settles direction faster than any right-hand rule.

SIGN

Track the charge

Positive and negative charges feel opposite forces in the same field. Decide the sign convention at the start and keep it.

SUPERPOSE

Add contributions

Fields and potentials from several sources add — fields as vectors, potentials as scalars. That difference makes potential the easier quantity whenever you have a choice.

CHECK

Test the limits

Let a distance go to infinity, a charge to zero, a speed to zero. The formula should reduce to something familiar, and relativity in particular must reduce to Newton.

03

Practice Plan

The mathematics here is no harder than PHY131H1 but the objects are less visible. Practice is what makes fields feel concrete.

01

Field before force

Find the field first, then multiply by the charge placed in it. Doing it in one step hides sign errors.

02

Prefer potential

Potentials are scalars and add without components. Reach for energy methods whenever the question allows.

03

Right-hand rule, deliberately

Practise it physically until it is automatic. Magnetism questions are lost on direction far more often than on arithmetic.

04

Take the lab seriously

A fifth of the hours are practical, and circuit measurement with uncertainty is examinable.

Course-wide challenge bank

These mix the ideas the way the final exam does.

Challenge 1 · Field versus potential

Two equal positive charges sit a distance $d$ apart. At the midpoint, what are the field and the potential?

Solution sketch
The fields are equal and opposite, so they cancel: $E = 0$. The potentials are both positive and add: $V = 2kq/(d/2)$, which is not zero. Field is a vector and can cancel; potential is a scalar and cannot. This pair is the clearest illustration of the difference.
Challenge 2 · Lenz's law

A magnet falls through a copper tube far more slowly than through air. Why?

Solution sketch
The changing flux induces currents in the tube, and by Lenz's law those currents oppose the change — producing a field that retards the magnet. The energy lost to slowing appears as heat in the copper. Energy is conserved; the magnet simply arrives later.
Challenge 3 · Which optics

When can light be treated as rays, and when must it be treated as waves?

Solution sketch
Rays suffice when obstacles and apertures are much larger than the wavelength — lenses, mirrors, shadows. Waves are required when they are comparable: slits, thin films, gratings. Interference and diffraction have no ray explanation at all.
Challenge 4 · Relativity check

A muon created high in the atmosphere reaches the ground despite a lifetime too short to allow it. Explain from both frames.

Solution sketch
From the ground: the muon's clock runs slow, so it lives long enough. From the muon: the atmosphere is length-contracted, so the trip is short enough. Different explanations, same outcome — which is exactly what relativity requires.
04

Resources

PHY132H1 — official calendar listing
Department of Physics

The calendar confirms the PHY132H1 topic list, the 36L/20P hours and the lab kit fee, but does not publish a current instructor textbook. Verify the assigned text, edition and problem numbers against the active syllabus each year.

PHY132H1 · INTRODUCTION TO PHYSICS II · U OF T PREREQUISITE: PHY131H1