Electric & Magnetic Fields

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Electric Charge

Charge is the property of matter responsible for the electric force; it is a scalar quantity measured in coulombs (C).
One coulomb is the charge carried by a current of one ampere in one second.
Charge is quantised: the charge on any object is a whole-number multiple of the elementary charge e = 1.60 × 10⁻¹⁹ C.
Protons are positive, electrons are negative, and neutrons are neutral; atoms are neutral when protons and electrons balance.
Like charges repel and opposite charges attract.
The law of conservation of charge states that the total charge in an isolated system remains constant — charge can be transferred but not created or destroyed.

Testing charge with perspex rods and watch glasses

Millikan's Oil Drop Experiment

Conducted by Millikan and Fletcher in 1909 to determine the value of the elementary charge.
A fine mist of oil is sprayed into a chamber; oil is used because it does not evaporate quickly, so the mass of the drops stays constant.
Drops become charged by friction as they leave the nozzle (or by ionisation with X-rays).
Without an electric field, drops fall under gravity and reach terminal velocity when air resistance equals gravitational force.
With an electric field, the upward electric force F = Eq can balance the gravitational force W = mg, allowing the charge to be found.
The experiment showed charge is always a multiple of 1.60 × 10⁻¹⁹ C, providing evidence for the quantisation of charge.

Static Electricity

Charging by friction: rubbing two insulators transfers electrons from one to the other, leaving one positive and the other equally negative.
Earthing (grounding) connects a body to the Earth so it discharges to 0 V; current takes the path of lower resistance.
Charging by electrostatic induction is the separation of charge caused by a nearby charged object without contact.
A neutral conducting sphere can be charged by induction: bring a charged rod near, earth the sphere, then remove the earth and rod.
Charging by contact transfers charge when two objects touch, reducing the potential difference between them (e.g. a 'shock' from a door handle).
Large potential differences can cause breakdown of air and a spark, risking electrocution or igniting flammable gases; a bonding line to Earth reduces this risk.

Coulomb's Law

Coulomb's law: the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of their separation.
F = kq₁q₂ / r², where k = 8.99 × 10⁹ N m² C⁻² and r is the distance between the centres of the charges.
Coulomb's constant is k = 1 / (4πε₀), where ε₀ is the permittivity of free space (8.85 × 10⁻¹² C² N⁻¹ m⁻²).
If q₁q₂ is positive the force is repulsive; if q₁q₂ is negative the force is attractive.
Coulomb's law applies only to point charges or spheres much smaller than their separation; it cannot be used for irregularly shaped objects.
The relative permittivity εᵣ = ε / ε₀ is the ratio of a material's permittivity to that of free space and has no units; for air εᵣ ≈ 1.

Electric Field Strength

An electric field is a region where a charge experiences a force; field strength is the force per unit positive test charge.
E = F / q, measured in N C⁻¹ or V m⁻¹; it is a vector directed away from positive charges and towards negative charges.
For a point charge, E = kq / r² — an inverse square law; a charged sphere behaves as a point charge with all charge at its centre.
Inside a charged conducting sphere the electric field strength is zero.
For a uniform field between parallel plates, E = V / d; a larger voltage gives a stronger field and a larger separation gives a weaker field.
Fields from multiple charges combine by vector addition: add magnitudes if in the same direction, subtract if opposite, or use Pythagoras for perpendicular fields.

Electric Field Lines

Field lines show the direction of the force on a positive test charge: they point from positive to negative and never cross.
In a uniform field the lines are equally spaced; in a radial field they spread out, so field strength decreases with distance.
Around a point charge, lines are radially outwards for positive and radially inwards for negative charges.
Field lines are always perpendicular to the surface of a conducting sphere, and the field inside is zero.
For two like charges, lines point away from both (or towards both) and there is a neutral point at the midpoint where the resultant field is zero.
The density of field lines represents field strength: closer lines mean a stronger field.

Electric Potential & Potential Energy

Electric potential at a point is the work done per unit charge bringing a small positive test charge from infinity to that point; it is a scalar measured in J C⁻¹ or V.
Potential is zero at infinity and is calculated using V = kQ / r.
Around a positive charge, potential is positive and increases as you move closer; around a negative charge, potential is negative and decreases as you move closer.
The potential always decreases in the direction of the field lines.
Electric potential energy is the work done in moving a charge between two points: Eₚ = qV.
For multiple charges, potentials combine by simple addition (they are scalars): V = kQ₁/r₁ + kQ₂/r₂.

Electric Potential Gradient & Equipotential Surfaces

The electric field strength equals the negative of the potential gradient: E = −ΔV / Δr.
Equipotential surfaces are surfaces where the potential is constant; no work is done moving a charge along an equipotential.
Equipotential lines are always perpendicular to electric field lines.
In a uniform field, equipotentials are straight, evenly spaced lines perpendicular to the field.
Around a point charge, equipotentials are concentric circles that become further apart as distance increases.

Magnetic Fields

A magnetic field is a region where a magnetic force acts on a moving charge or a current-carrying conductor.
The magnetic field around a straight current-carrying wire forms concentric circles in a plane perpendicular to the wire.
The direction of the field around a wire is given by the right-hand grip rule: thumb along the current, fingers curl in the field direction.
A solenoid produces a field like a bar magnet, with a North pole at the end where field lines emerge and a South pole where they enter.
Magnetic field lines run from North to South outside a magnet and form closed loops.

Magnetic field lines

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1.Which of the following best describes the shape of the electric field created by a point charge?
Easy
- ARadial
- BUniform
- CInverse
- DVector
2.An equipotential surface is always perpendicular to a field line:
Easy
- Afor both electric and gravitational fields
- Bfor electric fields only
- Cfor gravitational fields only
- Dfor neither electric nor gravitational fields
3.Which of the following statements about equipotential surfaces in a uniform electrostatic field is incorrect?
Medium
- AThe equipotential lines are straight
- BThe equipotential lines are evenly spaced
- CThe equipotential lines become progressively further apart
- DThe equipotential lines are perpendicular to the field lines
4.Which of the following is incorrect regarding the similarities between gravitational and electrostatic fields?
Medium
- AThe field lines around a point mass and a negative point charge are identical
- BThe work done in each field is either the product of mass and change in potential or charge and change in potential
- CThe gravitational potential and electric potential both have a 1/r relationship
- DThe gravitational and electrostatic forces are always attractive
5.Gravitational and electrostatic forces are similar in many ways. Which statements are correct about both? I. Both are always attractive. II. Both may be attractive or repulsive. III. Both follow an inverse square law. IV. The equations used to calculate these forces rely on knowing certain universal constants.
Medium
- AI and III only
- BIII and IV only
- CI, II, and III only
- DII, III, and IV only
6.The electric field strength inside a charged conducting sphere is zero.
Easy
True or false?
7.Electric field lines are always directed from a negative charge to a positive charge.
Easy
True or false?
8.Which of the following methods can transfer electric charge? (select all that apply)
Medium
- ACharging by friction
- BCharging by electrostatic induction
- CCharging by contact
- DCharging by electromagnetic induction
- ECharging by gravitational attraction

Thêm câu hỏi

9.Which of the following statements about the electric field between two parallel charged plates are correct? (select all that apply)
Medium
- AThe field is uniform between the plates
- BThe field lines are directed from the positive to the negative plate
- CThe field strength is given by E = V/d
- DThe field lines become further apart as the potential difference increases
- EThe field strength increases as the separation between the plates increases
10.Match each term with its correct definition or description.
Medium
- Electric field strength
- Electric potential
- Coulomb's law
- Force per unit positive charge
- Work done per unit charge moving from infinity
- Force between two point charges is proportional to product of charges and inversely proportional to square of separation
11.Arrange the steps of Millikan's oil drop experiment in the correct order.
Medium
- Oil drops are sprayed into a chamber and become charged by friction
- Drops fall under gravity and reach terminal velocity
- A potential difference is applied between the plates
- The electric force is adjusted until it balances the gravitational force
- The charge on the drop is calculated from the balanced forces
12.Which of the following statements about electric charge are correct? (select all that apply)
Medium
- ACharge is a scalar quantity.
- BThe coulomb is the charge carried by a current of one ampere in one second.
- CCharge can be created or destroyed in any process.
- DThe magnitude of charge on any object is a whole-number multiple of the elementary charge.
- EAn object can become positively charged by gaining protons through friction.
13.Oil is used instead of water in Millikan's oil drop experiment because it does not evaporate quickly, so the mass of the drops stays constant.
Easy
True or false?
14.Match each quantity with its correct SI unit.
Medium
- Electric charge
- Electric field strength
- Electric potential
- Coulomb constant k
- Permittivity of free space
- C
- N C⁻¹
- V
- N m² C⁻²
- C² N⁻¹ m⁻²
15.A current is passed through a wire running vertically upwards through a hole in a flat sheet of card. Which line correctly describes the magnetic field around the wire in terms of its direction and orientation relative to the card?
Medium
- AAnti-clockwise, in the same plane as the card
- BAnti-clockwise, perpendicular to the card
- CClockwise, in the same plane as the card
- DClockwise, perpendicular to the card
16.Two separated, identical conducting spheres X and Y have charges of −8 μC and +12 μC respectively. They are brought into brief contact and then separated. What is the final charge on each sphere?
Hard
- AX = −8 μC, Y = +12 μC
- BX = +10 μC, Y = +10 μC
- CX = +2 μC, Y = +2 μC
- DX = −4 μC, Y = +6 μC
17.Which of the following statements about the electric field inside and around a charged conducting sphere are correct? (select all that apply)
Medium
- AThe electric field strength is zero at all points inside the sphere.
- BThe field lines are perpendicular to the surface of the sphere.
- COutside the sphere the field is identical to that of a point charge of the same total charge at the centre.
- DThe field lines cross inside the sphere to show the cancellation of forces.
- EThe charge is concentrated at a single point on the surface.
18.Arrange the following steps of charging a neutral conducting sphere by electrostatic induction into the correct order.
Medium
- Bring a charged rod near the sphere without touching it.
- Connect the sphere to the Earth while the rod is still in place.
- Remove the Earth connection while the rod is still in place.
- Remove the charged rod.
19.Two charges Q₁ = q and Q₂ = 4q are separated by a distance r and exert a force of magnitude F on each other. By what factor does the magnitude of the force change if the charge on Q₁ doubles and the separation distance trebles?
Hard
- A1/9
- B2/3
- C2/9
- D9/2
20.A fine oil droplet of mass 4.9 × 10⁻¹⁵ kg is held stationary between two horizontal parallel plates separated by 8.0 mm when the potential difference between them is 640 V. What is the magnitude of the charge on the droplet? (g = 9.81 N kg⁻¹)
Medium
- A6.0 × 10⁻¹⁹ C
- B1.6 × 10⁻¹⁹ C
- C3.8 × 10⁻¹⁷ C
- D2.5 × 10⁻¹⁸ C
21.In a Millikan-type experiment, a charged oil drop is held stationary between two horizontal plates separated by 5.0 mm with a potential difference of 250 V. If the drop carries exactly two elementary charges (e = 1.60 × 10⁻¹⁹ C), what is the mass of the drop? (g = 9.81 N kg⁻¹)
Medium
- A1.6 × 10⁻¹⁵ kg
- B8.2 × 10⁻¹⁶ kg
- C4.1 × 10⁻¹⁶ kg
- D1.3 × 10⁻¹⁴ kg
22.In Millikan's experiment, the measured charges on several oil drops were 3.2 × 10⁻¹⁹ C, 4.8 × 10⁻¹⁹ C, 8.0 × 10⁻¹⁹ C and 1.12 × 10⁻¹⁸ C. What is the most likely value of the elementary charge suggested by these data?
Hard
- A1.6 × 10⁻¹⁹ C
- B3.2 × 10⁻¹⁹ C
- C8.0 × 10⁻²⁰ C
- D1.6 × 10⁻¹⁸ C
23.Two identical metal spheres carry charges of +6.0 μC and −2.0 μC. They are brought into brief contact and then separated. What is the charge on each sphere afterwards?
Medium
- A+2.0 μC
- B+4.0 μC
- C−2.0 μC
- D+1.0 μC
24.A metal sphere of radius 12 cm carries a uniform surface charge. The electric field strength at its surface is 2.0 × 10⁵ N C⁻¹. What is the total charge on the sphere? (k = 8.99 × 10⁹ N m² C⁻²)
Medium
- A3.2 × 10⁻⁷ C
- B3.2 × 10⁻⁵ C
- C2.7 × 10⁻⁸ C
- D3.8 × 10⁻⁶ C
25.A proton (charge +e, mass mₚ) is accelerated from rest through a potential difference V. Which expression gives its final speed?
Medium
- Av = √(2eV/mₚ)
- Bv = √(eV/mₚ)
- Cv = 2eV/mₚ
- Dv = √(eV/2mₚ)
26.A plotting compass is placed next to a vertical wire. With no current, the compass points North. A current is then passed upwards through the wire. In which direction does the compass needle now point?
Medium
- AEast
- BNorth
- CSouth
- DWest
27.A current flows through a solenoid. Which statement correctly describes the magnetic field produced?
Medium
- AThe field outside is like a bar magnet, with field lines from North to South; inside, the field is uniform and parallel to the axis
- BThe field is radial, spreading outwards from the axis in all directions
- CThe field lines outside run from South to North and inside run from North to South
- DThe field is zero everywhere except at the two ends of the solenoid
28.A plotting compass is placed at a point near a long straight vertical wire. When a current flows, the compass needle is deflected. Which statement about the magnetic field around the wire is correct?
Medium
- AThe field lines are concentric circles in the horizontal plane around the wire
- BThe field lines radiate outwards from the wire in the horizontal plane
- CThe field lines are parallel to the wire
- DThe field lines form concentric circles in the vertical plane containing the wire
29.A charged oil drop is held stationary between two horizontal parallel plates. Which changes would allow a drop with a larger charge (but the same mass) to remain stationary? (select all that apply)
Medium
- AIncrease the potential difference between the plates
- BDecrease the potential difference between the plates
- CReduce the separation between the plates
- DIncrease the separation between the plates
- EReverse the polarity of the plates
30.Two positive point charges +q and +4q are fixed a distance r apart. Which statements about the electric field on the line joining them are correct? (select all that apply)
Medium
- AThere is a neutral point between the charges where the resultant field is zero
- BThe neutral point lies closer to the smaller charge
- CThe neutral point lies closer to the larger charge
- DThe field midway between them is zero
- EThe resultant field at the neutral point is zero because the two fields are equal and opposite
31.The electric potential at a point due to a positive point charge increases as the distance from the charge decreases.
Easy
True or false?
32.The electric field strength between two parallel charged plates is inversely proportional to the potential difference between them.
Easy
True or false?
33.The electric potential inside a charged conducting sphere is constant and equal to the potential at its surface.
Medium
True or false?
34.Match each quantity with the correct expression.
Medium
- Electric force between two point charges
- Electric field strength due to a point charge
- Electric field strength between parallel plates
- Electric potential due to a point charge
- kq₁q₂/r²
- kQ/r²
- V/d
35.Arrange the following steps in order of increasing distance from a positive point charge, based on the electric potential at each distance.
Medium
- r = 0.10 m
- r = 0.20 m
- r = 0.40 m
- r = 0.80 m
36.Arrange the following steps of Millikan's oil drop experiment in the correct order.
Medium
- Oil is sprayed into the chamber and drops become charged by friction
- Drops pass between the two metal plates and are viewed through a microscope
- With no field, drops fall and reach terminal velocity under gravity
- A potential difference is applied so that the electric force balances the weight of a drop
- The charge on the drop is calculated from the balanced forces
37.Where is the neutral point (zero resultant field) located?
Medium
- AOn the line between the charges, closer to the +2.0 μC charge
- BOn the line between the charges, closer to the +8.0 μC charge
- CExactly midway between the two charges
- DOutside the two charges, on the side of the +2.0 μC charge
38.In Millikan's oil drop experiment, why is the oil drop viewed through a microscope rather than directly with the naked eye?
Medium
- AThe drops are very small and their motion must be observed precisely
- BThe oil drops emit light that is only visible through a microscope
- CThe microscope magnifies the electric field between the plates
- DThe microscope measures the charge on the drop directly
39.In a Millikan-type experiment, a charged oil drop is held stationary between two horizontal plates. If the potential difference is doubled while the plate separation is also doubled, what happens to the electric field strength between the plates?
Medium
- AIt remains the same
- BIt doubles
- CIt halves
- DIt quadruples
40.A student sets up two parallel plates separated by 2.0 cm with a potential difference of 400 V. The plates are horizontal. A small charged particle is suspended stationary between them. If the particle has a mass of 3.2 × 10⁻¹⁵ kg, what is the magnitude of its charge? (g = 9.8 N kg⁻¹)
Medium
- A1.6 × 10⁻¹⁸ C
- B1.6 × 10⁻¹⁶ C
- C6.4 × 10⁻¹⁸ C
- D3.2 × 10⁻¹⁵ C
41.Complete the sentence about the definition of electric field strength.
Easy
Electric field strength is defined as the ____ per unit ____ experienced by a small positive test charge placed at that point.
42.Name the three methods by which electric charge can be transferred.
Medium
The three methods are charging by ____, charging by ____, and charging by ____.
43.What is the SI unit of electric charge?
Easy
44.A particle has a charge of 3.2 × 10⁻¹⁹ C. How many elementary charges does this correspond to? (e = 1.60 × 10⁻¹⁹ C)
Medium
45.Two parallel metal plates are separated by 3.5 cm and have a potential difference of 7.9 kV between them. Calculate the magnitude of the electric force acting on a point charge of 2.6 × 10⁻¹⁵ C placed between the plates. Give your answer in newtons to 2 significant figures.
Medium
46.Complete the definition of electric potential by filling in the gaps.
Easy
The electric potential at a point is the ____ done per unit ____ in taking a small positive test charge from ____ to that point.
47.Calculate the charge stored on the dome. Give your answer in coulombs to 2 significant figures.
Hard
48.Calculate the potential at a distance of 30 cm from the surface of the dome. Give your answer in volts to 2 significant figures.
Hard
49.Two parallel plates are separated by 4.0 cm and have a potential difference of 6.0 kV between them. Calculate the electric force on a point charge of 3.0 × 10⁻¹⁵ C placed between the plates. Give your answer in newtons.
Medium
50.An α particle (charge +2e, e = 1.60 × 10⁻¹⁹ C) is placed 3.0 mm from a gold nucleus (charge +79e) in a vacuum. Calculate the magnitude of the electric force between them. (k = 8.99 × 10⁹ N m² C⁻²) Give your answer in newtons.
Medium
51.A charge of 5.0 μC is placed at a point where the electric field strength is 4.0 × 10⁴ N C⁻¹. Calculate the magnitude of the force on the charge. Give your answer in newtons.
Medium
52.Complete the sentence about the electric field between two parallel plates.
Medium
The electric field strength between two parallel plates is equal to the potential difference divided by the ____ between the plates, and its unit is ____.
53.Explain how an initially neutral conducting sphere can become charged by electrostatic induction when a negatively charged rod is brought nearby.
Hard
54.Explain how the results of Millikan's oil drop experiment provide evidence that electric charge is quantised.
Hard
55.A student sets up two parallel plates with a potential difference V and separation d. Explain why the electric field between them is uniform, and describe how the field lines would change if V were doubled while d stayed the same.
Hard
56.An initially neutral conducting sphere is charged by electrostatic induction using a negatively charged rod. Describe the sequence of events, including the role of earthing, and explain why the sphere ends up positively charged.
Hard
57.Describe how the electric field between two parallel plates can be made uniform, and explain how the field strength depends on the potential difference and plate separation.
Hard
58.A particle has a charge of 3.2 × 10⁻¹⁹ C. How many elementary charges does this correspond to? (e = 1.60 × 10⁻¹⁹ C)
Medium
- A4 elementary charges
- B3 elementary charges
- C1 elementary charges
- D2 elementary charges
59.Two parallel metal plates are separated by 3.5 cm and have a potential difference of 7.9 kV between them. Calculate the magnitude of the electric force acting on a point charge of 2.6 × 10⁻¹⁵ C placed between the plates. Give your answer in newtons to 2 significant figures.
Medium
- A1 N
- B5.9e-10 N
- C-1 N
- D2 N
60.Calculate the charge stored on the dome. Give your answer in coulombs to 2 significant figures.
Hard
- A-1 C
- B0.000004 C
- C1 C
- D2 C
61.Calculate the potential at a distance of 30 cm from the surface of the dome. Give your answer in volts to 2 significant figures.
Hard
- A80000 V
- B88000 V
- C96000 V
- D72000 V
62.Two parallel plates are separated by 4.0 cm and have a potential difference of 6.0 kV between them. Calculate the electric force on a point charge of 3.0 × 10⁻¹⁵ C placed between the plates. Give your answer in newtons.
Medium
- A-1 N
- B4.5e-10 N
- C1 N
- D2 N
63.An α particle (charge +2e, e = 1.60 × 10⁻¹⁹ C) is placed 3.0 mm from a gold nucleus (charge +79e) in a vacuum. Calculate the magnitude of the electric force between them. (k = 8.99 × 10⁹ N m² C⁻²) Give your answer in newtons.
Medium
- A2 N
- B1 N
- C4e-21 N
- D-1 N
64.A charge of 5.0 μC is placed at a point where the electric field strength is 4.0 × 10⁴ N C⁻¹. Calculate the magnitude of the force on the charge. Give your answer in newtons.
Medium
- A-0.8 N
- B0.2 N
- C1.2 N
- D2.2 N

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