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IB Physics HL/Notes/D.2 Electric and magnetic fields

IB Physics HLD.2 Electric and magnetic fieldsNotes

Map Electric charge forces

Electric charge force questions are sign-and-direction questions before they are calculation questions. The magnitude may come from Coulomb’s law, but the arrow comes from the charge signs: like charges push apart, opposite charges pull together.

Positive and negative are the two signs of electric charge; like charges repel and unlike charges attract.
The electrostatic force between two point charges acts along the straight line joining their centres.
The two charges exert forces on each other that are equal in magnitude and opposite in direction.
A positive test charge is the convention used to define electric field direction.
Before using equations, decide whether the force is attractive or repulsive from the signs.

Label the force-direction features on the two-charge diagram.

Label
Labels
4

State the force direction between two charged particles for like and unlike signs.

Giving only the magnitude rule and not saying whether the force is attractive or repulsive.

State the force direction between two charged particles for like and unlike signs.

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Map Coulomb’s law

Coulomb’s law is the electric-force analogue of an inverse-square law. In exam answers, build the magnitude cleanly and then add the direction in words. The sign product is useful for reasoning, but the physical arrow should be described as attraction or repulsion.

Coulomb’s law for point charges is F = kq1q2/r^2, where k = 1/(4πε0).
For force magnitude, use |F| = k|q1q2|/r^2 and express the answer in newtons.
The separation r is the distance between the charges, treated as point charges.
The force is repulsive for charges with the same sign and attractive for charges with opposite signs.
Doubling r reduces the force magnitude by a factor of four.

Assemble Coulomb’s law and the sign-direction sentence.

Formula
Target formula F = kq1q2/r^2
F
electrostatic force magnitude
N
k
Coulomb constant, 1/(4πε0)
N m^2 C^-2
q1
first point charge
C
q2
second point charge
C
r
separation between charges
m
1Use the product of charge magnitudes and the inverse-square separation.|F| = k|q1q2|/r^2
2Name the electrostatic constant.k = 1/(4πε0)
3Use signs to state attraction or repulsion.same signs repel; opposite signs attract
4Check inverse-square scaling.r doubled -> F/4

Two point charges are separated by distance r. State Coulomb’s law and explain how charge signs affect direction.

Forgetting that r is squared or failing to describe attraction or repulsion.

Two point charges are separated by distance r. State Coulomb’s law and explain how charge signs affect direction.

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Map Charge conservation

A conservation explanation is a before-and-after account. You decide what system is isolated, add the charge before, add the charge after, and make the totals match. This is separate from quantization, which says the allowed amounts come in packets of e.

Charge is conserved: the total charge of an isolated system remains constant.
Charging processes transfer charge between objects or between an object and Earth; they do not create net charge from nothing.
In most solid charging examples, electrons are the mobile charges that move.
If one object gains negative charge, another part of the system must lose the same amount of negative charge or gain positive charge by electron loss.
Charge is also quantized, so net charge changes in integer multiples of the elementary charge e.

Repair the three charge-conservation statements.

Spot Errors

Explain why charging an object by rubbing does not violate conservation of charge.

Saying charge is created rather than transferred.

Explain why charging an object by rubbing does not violate conservation of charge.

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Map Millikan experiment

The exam-worthy point is the evidence chain. A charged drop in a known electric field has a measurable force balance; repeated measurements reveal that the charge values are not continuous. They occur as multiples of one elementary charge.

Millikan’s oil-drop experiment measured charges on tiny oil drops.
An electric field was adjusted so electric force could balance the weight of a charged drop.
From the field and drop properties, the charge on each drop could be inferred.
The measured charges were integer multiples of the elementary charge e.
The key syllabus conclusion is charge quantization: q = ne, where n is an integer.

Match each Millikan cue to its role in the argument.

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State what the Millikan oil-drop experiment demonstrated about electric charge.

Describing only that drops float, without stating charge quantization.

State what the Millikan oil-drop experiment demonstrated about electric charge.

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Map Charge transfer

Practice

Charge-transfer questions are process-order questions. Look for contact, for a nearby charged object causing separation, and for an earthing connection. The answer should name the method and track electrons through the steps.

Charging by friction transfers electrons when two materials are rubbed together.
Charging by contact transfers charge when a charged object touches another object.
Charging by induction separates charge within a conductor without direct contact from the charged object.
Earthing provides a path for electrons to flow between the object and Earth.
In induction, the final charge of the conductor is opposite to the nearby inducing charge if the grounding step is completed before the charged object is removed.

Sort each charging cue into the correct mechanism.

Sort
Unsorted
5
friction
0
contact
0
induction
0
earthing
0

Describe how a neutral conducting sphere can be charged by induction using a negatively charged rod.

Removing the rod before disconnecting Earth, or saying the rod transfers charge by touching.

Describe how a neutral conducting sphere can be charged by induction using a negatively charged rod.

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Map Electric field strength

Electric field strength tells you what force each coulomb of positive test charge would feel. That convention matters: a negative charge placed in the field experiences force opposite to E.

Electric field strength E is the force per unit positive test charge: E = F/q.
The unit N C^-1 is equivalent to V m^-1.
The direction of E is the direction of the force on a positive test charge.
For a point charge Q, the field magnitude is E = k|Q|/r^2.
Field direction is away from a positive source charge and toward a negative source charge.

Build E from force per unit positive test charge.

Formula
Target formula E = F/q
E
electric field strength
N C^-1 or V m^-1
F
force on the test charge
N
q
positive test charge used to define the field
C
Q
source charge for a radial field
C
r
distance from the source charge
m
1Start with force per unit positive test charge.E = F/q
2Convert the unit.N C^-1 = V m^-1
3For a point source charge, combine with Coulomb’s law.E = kQ/r^2 for magnitude use k|Q|/r^2
4State direction using the positive-test-charge convention.away from +Q, toward -Q

Define electric field strength and state the direction of an electric field.

Defining field direction using the force on an electron.

Define electric field strength and state the direction of an electric field.

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Map Electric field lines

A field-line diagram is not decoration; it encodes field direction and relative field strength. The arrows come from the positive-test-charge convention. Density represents strength. Crossed lines would imply two different field directions at the same point.

Electric field lines point in the direction of the force on a positive test charge.
Lines leave positive charges and enter negative charges.
Closer spacing of field lines represents a stronger electric field.
Field lines never cross because a point has only one field direction.
Between large parallel plates, the central field is approximately uniform: parallel, equally spaced lines from the positive plate to the negative plate.

Drag the labels to the electric-field-line diagram.

Label
Labels
5

Sketch electric field lines for a positive and a negative point charge and explain what line spacing shows.

Drawing arrows into a positive charge or treating line count as exact numerical field strength.

Sketch electric field lines for a positive and a negative point charge and explain what line spacing shows.

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Read the Field-Line Pattern

Reading a field-line diagram means making claims from the drawing: direction comes from the local tangent and arrows, while strength comes from line density. The diagram does not show a particle track unless a question explicitly says a charge follows it.

At any point, the electric field direction is tangent to the field line and follows the arrow.
A positive test charge accelerates in the direction of E if no other forces are considered.
A negative charge feels force opposite to E.
The field is stronger where field lines are more closely spaced.
Field lines are a representation of the field, not the actual paths that charges must follow.

Read strength and direction from the field-line pattern.

Graph

Electric field-line diagram with points A, B, and C. Lines are closest at A, wider at B, and nearly parallel at C.

1identify strongest field from line density
2state direction from arrows or tangent
3compare force on positive and negative charges

Use an electric field-line diagram to identify where the field is strongest and state the force direction on an electron.

Saying an electron feels force in the field direction.

Use an electric field-line diagram to identify where the field is strongest and state the force direction on an electron.

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Analyze Parallel-plate field

Parallel plates are the cleanest electric-field model. The field is treated as constant in magnitude and direction between the plates, so potential changes linearly with distance and E = V/d.

Between large oppositely charged parallel plates, the central electric field is approximately uniform.
Uniform field lines are straight, parallel, equally spaced, and directed from the positive plate to the negative plate.
For plate potential difference V and separation d, E = V/d.
The unit V m^-1 is equivalent to N C^-1.
The uniform-field model ignores fringing near the plate edges.

Assemble the parallel-plate field model.

Formula
Target formula E = V/d
E
uniform electric field strength
V m^-1 or N C^-1
V
potential difference between plates
V
d
plate separation
m
q
charge placed in the field
C
1State the model condition.large parallel plates, central region, fringing ignored
2Field is potential difference per separation.E = V/d
3State field direction.from positive plate to negative plate
4If a charge is placed in the field, link to force.F = qE

A potential difference is applied across two parallel plates. State the expression for the electric field and describe the field-line pattern.

Using inverse-square radial-field language for plates.

A potential difference is applied across two parallel plates. State the expression for the electric field and describe the field-line pattern.

Choose

Map Magnetic field lines

Magnetic field-line questions are pattern recognition plus direction rule. For magnets, use north-to-south outside the magnet. For wires and coils, use the right-hand grip rule with conventional current.

Magnetic field lines outside a bar magnet go from the north pole to the south pole.
Field lines form closed loops; inside the magnet they continue from south to north.
A straight current-carrying wire has concentric circular magnetic field lines around it.
The right-hand grip rule gives the circular field direction: thumb in conventional current direction, fingers curl with B.
A current loop or solenoid produces a field pattern similar to a bar magnet, with an approximately uniform field inside a long solenoid.

Label the standard magnetic field-line patterns.

Label
Labels
5

Sketch the magnetic field around a straight current-carrying wire and state the rule used to determine its direction.

Using electric-field-line rules such as starting at positive and ending at negative.

Sketch the magnetic field around a straight current-carrying wire and state the rule used to determine its direction.

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Electric potential energy

Potential energy belongs to a particular charge, while potential belongs to the field point. Once V is known, multiply by q to get E_p. Be careful with negative charges: the same potential change gives the opposite sign of energy change.

Electric potential energy E_p is the energy a charge has because of its position in an electric field.
Electric potential V is energy per unit charge, so E_p = qV.
For a move between two potentials, ΔE_p = qΔV.
The sign of ΔE_p depends on both the sign of q and the sign of ΔV.
Work done by the electric field is W_field = -ΔE_p.

Connect electric potential to potential energy.

Formula
Target formula E_p = qV
E_p
electric potential energy
J
q
charge placed in the field
C
V
electric potential at the point
V or J C^-1
ΔV
potential difference for a move
V
1Potential is energy per unit charge.V = E_p/q
2Rearrange for energy.E_p = qV
3For a move between two potentials.ΔE_p = qΔV
4Relate to work done by the field.W_field = -ΔE_p

A charge moves between two electric potentials. State how to calculate the change in electric potential energy.

Using ΔEp = qE instead of qΔV.

A charge moves between two electric potentials. State how to calculate the change in electric potential energy.

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Map Two-charge potential energy

This formula is the energy version of the two-charge interaction. The sign matters physically: positive potential energy for repelling like charges, negative potential energy for attracting unlike charges when zero is at infinity.

For two point charges, E_p = kq1q2/r when zero potential energy is chosen at infinity.
Like charges give positive potential energy because q1q2 is positive.
Unlike charges give negative potential energy because q1q2 is negative.
As r increases, E_p approaches zero.
External work is required to bring like charges closer together slowly; energy is released when unlike charges move closer.

Assemble the two-charge potential-energy model.

Formula
Target formula E_p = kq1q2/r
E_p
electric potential energy of the two-charge system
J
k
Coulomb constant
N m^2 C^-2
q1
first point charge
C
q2
second point charge
C
r
separation between charges
m
1Use the two-charge energy formula.E_p = kq1q2/r
2State the reference level.E_p = 0 at infinity
3Interpret like-charge sign.q1q2 > 0 -> E_p > 0
4Interpret unlike-charge sign.q1q2 < 0 -> E_p < 0

State the electric potential energy of two point charges and explain why it can be negative.

Dropping the signs of the charges.

State the electric potential energy of two point charges and explain why it can be negative.

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Electric potential as scalar

Potential tells you energy per coulomb at a point. Unlike electric field, it does not point anywhere. This makes multi-charge problems easier: calculate each potential with its sign and add the numbers.

Electric potential V at a point is electric potential energy per unit charge: V = E_p/q.
The unit of potential is J C^-1, called the volt.
Electric potential is scalar: it has a sign but no direction.
Potentials from multiple source charges add algebraically, not vectorially.
Electric field is vector; potential is scalar, so do not use arrows for V.

Match each electric-potential cue to the correct scalar idea.

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Reasons
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Define electric potential and explain how potentials from several charges combine.

Adding potentials as vectors or assigning a direction to potential.

Define electric potential and explain how potentials from several charges combine.

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Electric potential

Point-charge potential looks like the energy-per-charge version of Coulomb’s interaction. Keep the sign of Q and add contributions as scalars. The result is a voltage value at a point, not an arrow.

The electric potential due to a point charge Q is V = kQ/r with zero potential at infinity.
Potential is positive around a positive source charge and negative around a negative source charge.
Potential magnitude decreases as distance r increases.
For several point charges, total potential is the algebraic sum of kQ/r terms.
The field direction cannot be read from the sign of V alone; use potential gradient or field lines for E.

Assemble the point-charge potential expression.

Formula
Target formula V = kQ/r
V
electric potential at a point
V
k
Coulomb constant
N m^2 C^-2
Q
source charge
C
r
distance from source charge
m
1Use point-charge potential with sign.V = kQ/r
2State the reference level.V = 0 at infinity
3Interpret source-charge sign.+Q -> positive V; -Q -> negative V
4For multiple charges, add scalar contributions.V_total = Σ(k Qi/ri)

Calculate the electric potential at a point due to several point charges. State the rule used to combine contributions.

Adding only magnitudes and losing the sign of negative charges.

Calculate the electric potential at a point due to several point charges. State the rule used to combine contributions.

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Electric potential gradient

The potential-gradient relation connects graph shape to field. A flat potential region has zero field. A steep potential change has large field. The negative sign is directional: a positive test charge is pushed toward lower potential.

In one dimension, electric field is the negative gradient of electric potential: E = -dV/dr.
The magnitude of E is the magnitude of the potential gradient.
The minus sign means electric field points in the direction of decreasing potential for a positive test charge.
A steeper V-r graph means a stronger electric field.
For a uniform field between plates, V changes linearly with distance and E = -ΔV/Δr.

Interpret electric field from a potential graph.

Graph

A V against x graph has a steep negative slope in region A, a shallow negative slope in region B, and a flat region C.

1compare field magnitudes from slope magnitudes
2use E = -dV/dx
3interpret the sign of the gradient

A graph of electric potential against distance is provided. Explain how to determine the electric field strength from the graph.

Using the potential value at the point instead of the graph gradient.

A graph of electric potential against distance is provided. Explain how to determine the electric field strength from the graph.

Choose

Map Work in electric fields

Work questions need a named agent. The electric field’s work is negative the potential-energy change. An external agent moving the charge slowly does work equal to the energy change. Along an equipotential, the potential difference is zero, so the work is zero.

For a charge q moving through potential difference ΔV, ΔE_p = qΔV.
The work done by the electric field is W_field = -ΔE_p = -qΔV.
If a charge is moved slowly by an external force with no change in kinetic energy, W_external = ΔE_p.
Moving along an equipotential has ΔV = 0, so no work is done by the field.
For positive charges, the electric field does work as they move to lower potential; for negative charges the sign reverses.

Repair the work-energy statements for electric fields.

Spot Errors

A charge is moved between two points of different electric potential. Explain how to find the work done by the electric field.

Not distinguishing work done by the field from work done by an external force.

A charge is moved between two points of different electric potential. Explain how to find the work done by the electric field.

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Map Electric equipotentials

Equipotentials are the contour lines of electric potential. They show equal voltage values. Moving along one does not change potential energy, so the electric field does no work along that path.

An equipotential is a line or surface on which electric potential is constant.
Moving a charge along an equipotential gives ΔV = 0.
Because ΔE_p = qΔV, no work is done by the electric field along an equipotential.
Around a single point charge, equipotentials are concentric circles in a plane or spherical surfaces in space.
Between uniform parallel plates, equipotentials are parallel to the plates.

Label the equipotential features.

Label
Labels
4

Define an equipotential and explain why no work is done moving a charge along it.

Adding arrows to equipotential lines or treating them as field lines.

Define an equipotential and explain why no work is done moving a charge along it.

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Map Equipotentials and electric fields

Equipotentials and field lines are two representations of the same field. Equipotentials show constant voltage; field lines show direction of steepest decrease in V for a positive test charge. Their perpendicular relationship is one of the safest diagram checks in D.2.

Electric field lines cross equipotential lines or surfaces at right angles.
If E had a component along an equipotential, the field would do work along a path with ΔV = 0, which is impossible.
Electric field points in the direction of decreasing electric potential for a positive test charge.
The closer the equipotential lines are, the larger the potential gradient and the stronger the electric field.
This is the diagram version of E = -dV/dr.

Label the relationship between field lines and equipotentials.

Label
Labels
4

Explain the relationship between electric field lines and equipotential surfaces.

Saying field lines are parallel to equipotentials.

Explain the relationship between electric field lines and equipotential surfaces.

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Retrieve the Core D.2 Electric and magnetic fields Model

Review

This summary card is a retrieval net for SL D.2. It asks students to move between force rules, charge conservation, transfer mechanisms, electric field diagrams, uniform-field equations, and magnetic field-line patterns without importing gravitational or motion language.

Like charges repel and unlike charges attract; Coulomb’s law gives |F| = k|q1q2|/r^2 for point charges.
Total charge is conserved in an isolated system, and charge is quantized in integer multiples of e.
Charging occurs by friction, contact, induction, and earthing through electron transfer or redistribution.
Electric field strength is E = F/q, directed as the force on a positive test charge; point charge fields follow E = kQ/r^2 in magnitude.
Electric field lines go from positive to negative, closer lines mean stronger E, and parallel plates give an approximately uniform field with E = V/d.
Magnetic field diagrams include bar magnets, straight wires, loops, and solenoids; current-field direction uses the right-hand grip rule.

Match each core D.2 cue to the model it should trigger.

Match
Reasons
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Summarize the core D.2 electric and magnetic field models.

Listing formulas without conditions, directions, or diagram conventions.

Summarize the core D.2 electric and magnetic field models.

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Retrieve the HL D.2 Electric and magnetic fields Model

Review

HL D.2 is mostly about energy and representation discipline. Keep potential scalar, field vector, signs explicit, and the work agent named. Equipotentials then become easy: constant V means zero ΔE_p and field lines must be perpendicular.

Electric potential energy and potential are linked by E_p = qV and ΔE_p = qΔV.
For two point charges, E_p = kq1q2/r with zero at infinity.
Electric potential due to a point charge is V = kQ/r and potentials add algebraically because potential is scalar.
Electric field is the negative potential gradient: E = -dV/dr in one dimension; steeper potential graphs mean stronger field.
Work done by the electric field is W_field = -ΔE_p; slow external work is ΔE_p.
Equipotentials have constant V, no work is done along them, and electric field lines cross them at right angles.

Match each HL D.2 cue to its formula or diagram relationship.

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Reasons
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Summarize the HL D.2 potential and equipotential model.

Mixing scalar potential with vector field or forgetting the work sign convention.

Summarize the HL D.2 potential and equipotential model.

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