Electric & Magnetic Fields

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Electric Charge

Charge is the property of matter responsible for the electric force; its unit is the coulomb (C), defined as the charge carried by a current of one ampere in one second.
Charge is a scalar quantity and is quantised — the charge on any object is always a whole-number multiple of the elementary charge e = 1.60 × 10⁻¹⁹ C.
Atoms contain negative electrons, positive protons and neutral neutrons; most everyday objects are neutral because protons and electrons balance.
An object becomes charged by gaining or losing electrons; it is a common misconception that positive charge is 'gained' — objects become positive only by losing electrons.
Opposite charges attract, like charges repel — remember 'opposites 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.
When charged objects are brought into contact, charge is shared until evenly distributed — the final charge on each identical object is the average of the initial charges.

Testing charge with perspex rods and watch glasses

Millikan's Oil Drop Experiment

Conducted by Millikan and Fletcher in 1909, this experiment determined the value of the fundamental elementary charge.
A fine mist of oil (not water, because it does not evaporate quickly, keeping the mass constant) is sprayed into a chamber and charged by friction or by X-rays.
The drops pass between two metal plates and are viewed through a microscope.
Without an electric field, drops fall under gravity and reach terminal velocity when air resistance equals gravitational force.
With an electric field, charged drops rise when the upward electric force exceeds the gravitational force; the electric force is F = Eq and the weight is W = mg.
By equating the electric and gravitational forces, the fundamental charge was found to be 1.60 × 10⁻¹⁹ C — the magnitude of charge on any object is a multiple of this value, providing evidence for the quantisation of charge.

Static Electricity

Charge can be transferred by friction, electrostatic induction and contact.
Charging by friction: when two insulators are rubbed together, electrons transfer from one to the other — the material losing electrons becomes positive, the one gaining electrons becomes negative.
Earthing (grounding) connects a body to the Earth so it discharges until it has a potential of 0 V; current takes the path of lower resistance, so a copper earth wire protects a person.
Electrostatic induction is the separation of charge caused by a nearby charged object without physical contact (not the same as electromagnetic induction).
A neutral conducting sphere can be charged by induction: a charged rod is brought near (without touching), the sphere is grounded, then the rod and earth connection are removed leaving excess charge.
Charging by contact occurs when a charged object touches another object, allowing electrons to flow to reduce the potential difference — e.g. the 'shock' felt when touching a doorknob.
Dangers of static electricity: a large potential difference can cause breakdown of air and a spark, risking electrocution (lightning) or igniting flammable gases — reduced by connecting a bonding line to Earth, e.g. when refuelling aeroplanes.

Coulomb's Law

Coulomb's law states that 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.
The force is calculated using F = kq₁q₂ / r², where k is the Coulomb constant (8.99 × 10⁹ N m² C⁻²), q₁ and q₂ are the magnitudes of the charges, and r is the distance between their centres.
Coulomb's law is analogous to Newton's law of gravitation — both follow an inverse square law with separation.
The Coulomb constant is given by k = 1 / (4πε₀), where ε₀ is the permittivity of free space (8.85 × 10⁻¹² C² N⁻¹ m⁻²).
If the product q₁q₂ is positive, the charges repel; if negative, they attract — unlike gravity, which is only attractive.
When a material is between the charges, k = 1 / (4πε), where ε = εᵣε₀; relative permittivity εᵣ is the ratio of the permittivity of a material to that of free space and has no units.
Coulomb's law only applies to charged spheres whose size is much smaller than their separation (the point charge approximation), with r measured from the centres.

Electric Field Strength

An electric field is a region of space in which an electric charge experiences a force.
Electric field strength at a point is defined as the force per unit charge experienced by a small positive test charge placed at that point: E = F / q, measured in N C⁻¹.
Electric field strength is a vector quantity, always directed away from a positive charge and towards a negative charge.
The field due to a point charge follows an inverse square law: E = kq / r², decreasing with the square of the distance.
A charged sphere behaves like a point charge with all its charge at the centre; inside the sphere the electric field strength is zero.
Electric fields from multiple charges are combined by vector addition — add fields in the same direction, subtract opposite ones, or use Pythagoras' theorem for fields at right angles.
For a uniform field between parallel plates, E = V / d, where V is the potential difference and d the separation; the field is directed from the positive plate to the negative plate.
The units V m⁻¹ and N C⁻¹ for electric field strength are equivalent; if one plate is earthed it has a voltage of 0 V.

Electric Field Lines

Field lines represent the direction and magnitude of an electric field; they are always directed from positive to negative charge and never cross.
The closer the field lines, the stronger the field; the further apart, the weaker the field.
In a uniform field (between parallel plates), field lines are equally spaced and the field strength is constant at all points.
In a radial field (around a point charge), field lines spread out with distance, so field strength and force decrease with distance.
Around a positive point charge, field lines are radially outwards; around a negative charge, radially inwards.
Field lines are always perpendicular to the surface of a conducting sphere, and the field inside the sphere is zero.
Between two opposite charges, field lines connect the surfaces (attraction); between two like charges, field lines do not connect and there is a neutral point at the midpoint where the resultant field is zero.
The density of field lines represents field strength — a higher potential difference across parallel plates gives denser lines and a stronger field.

Magnetic Fields

A magnetic field is a region of space in which a magnetic pole experiences a force; it is created by moving electric charge or by permanent magnets — a stationary charge does not produce a magnetic field.
Magnetic flux density B is defined as the number of magnetic field lines passing through a region of space per unit area, measured in teslas (T).
One tesla is the flux density that causes a force of 1 N on a 1 m wire carrying a current of 1 A at right angles to the field.
Magnetic field lines are directed from the north pole to the south pole; the field is strongest where lines are closest together, and field lines never cross.
Two like poles repel and two opposite poles attract; a uniform magnetic field is represented by equally spaced parallel lines, created when two opposite poles are held close together.
The Earth's magnetic field acts like a bar magnet — a compass points to the Earth's magnetic south pole, which is the geographic north pole.

Magnetic field lines

Magnetic Fields from Currents

Magnetic fields are formed wherever a current flows, such as in long straight wires, long solenoids and flat circular coils.
Around a current-carrying wire, field lines are circular rings centred on the wire; they are closest together near the wire (strongest) and spread out with distance (weaker).
Reversing the current reverses the direction of the magnetic field.
The right-hand grip rule determines the field direction: point the right thumb in the direction of the (conventional) current and the curled fingers give the direction of the magnetic field.
A solenoid (coil of wire) increases the magnetic flux density by adding more turns of wire into a smaller region; one end becomes a north pole and the other a south pole.
The field lines around a solenoid are similar to those of a bar magnet — emerging from the north pole and returning to the south pole.
For a solenoid, the right-hand grip rule is applied with curled fingers in the direction of current flow around the coil and the thumb pointing towards the north pole.
A flat circular coil is equivalent to one coil of a solenoid; the field direction is found using the right-hand grip rule on the straight part of the coil.

Magnetic field around a current-carrying wire, showing field lines and the right-hand grip rule.

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1.What is the unit of electric charge?
Easy
- ACoulomb (C)
- BAmpere (A)
- CVolt (V)
- DNewton (N)
2.Which of the following correctly describes the electric force between two charges of the same type?
Easy
- AAttractive
- BRepulsive
- CZero
- DPerpendicular to the line joining them
3.Charge can be created or destroyed in an isolated system.
Easy
True or false?
4.Which of the following is the correct definition of electric field strength at a point?
Easy
- AThe force per unit charge experienced by a small positive test charge placed at that point
- BThe force per unit mass experienced by a small test mass placed at that point
- CThe force per unit charge experienced by a small negative test charge placed at that point
- DThe product of the force and the charge at that point
5.Which of the following best describes what is meant by the strength of an electric field?
Easy
- AThe force per unit charge at a point in the field
- BThe total number of field lines in the field
- CThe potential difference between two points in the field
- DThe distance between two adjacent field lines
6.A negative ion is placed in a uniform electric field. In which direction does the electrostatic force act on the ion?
Medium
- AOpposite to the direction of the electric field lines
- BIn the same direction as the electric field lines
- CPerpendicular to the electric field lines
- DThe force is zero because the ion is negative
7.An α particle approaches an aluminium nucleus. Which of the following describes the nature of the force between them?
Medium
- ARepulsive, because both particles are positively charged
- BAttractive, because the α particle is negative and the nucleus is positive
- CRepulsive, because the α particle is negative and the nucleus is positive
- DAttractive, because both particles are positively charged
8.A stationary electric charge produces a magnetic field.
Medium
True or false?

Thêm câu hỏi

9.Which of the following statements is the correct definition of magnetic flux density?
Medium
- AThe number of magnetic field lines passing through a region of space per unit area
- BThe force per unit charge experienced by a small positive test charge
- CThe total number of magnetic field lines around a magnet
- DThe force per unit length on a wire carrying a current of 1 A
10.A charged conducting sphere is isolated. Which of the following is true about the electric field inside the sphere?
Medium
- AThe electric field is zero at all points inside the sphere
- BThe electric field is uniform and non-zero inside the sphere
- CThe electric field is maximum at the centre of the sphere
- DThe electric field is directed radially outwards inside the sphere
11.Two parallel plates are separated by a distance d and have a potential difference V between them. Which equation gives the magnitude of the electric field strength between the plates?
Medium
- AE = V / d
- BE = d / V
- CE = V × d
- DE = qV / d
12.Which of the following statements about electric field lines is correct?
Medium
- AElectric field lines are always directed from a positive charge to a negative charge
- BElectric field lines are always directed from a negative charge to a positive charge
- CElectric field lines can cross each other at neutral points
- DElectric field lines are always equally spaced in a radial field
13.A free electron is incident in the space between two parallel charged plates and is deflected as it moves between them. Which of the following best explains the shape of its path?
Hard
- AThe electric field exerts a constant force on the electron, causing a parabolic path
- BThe electric field exerts a force that increases with distance, causing a circular path
- CThe electric field exerts no force on the electron, so it moves in a straight line
- DThe magnetic field between the plates deflects the electron in a circular path
14.Which of the following statements about Coulomb's law are correct? (select all that apply)
Medium
- AThe electric force between two point charges is directly proportional to the product of the charges
- BThe electric force between two point charges is inversely proportional to the square of their separation
- CThe electric force between two point charges is directly proportional to their separation
- DCoulomb's law can be applied to charges distributed on irregularly-shaped objects
- EThe electric force between two point charges can be attractive or repulsive
15.Which of the following are valid methods by which an object can become charged? (select all that apply)
Hard
- ACharging by friction
- BCharging by electrostatic induction
- CCharging by contact
- DCharging by heating
- ECharging by cooling
16.In a uniform electric field, the electric field strength is the same at all points.
Medium
True or false?
17.Magnetic field lines are directed from the south pole to the north pole outside a magnet.
Medium
True or false?
18.Match each term with its correct definition.
Medium
- Electric field strength
- Magnetic flux density
- Coulomb's law
- Permittivity
- Force per unit positive charge at a point
- Number of magnetic field lines per unit area
- Electric force between two point charges
- Measure of resistance to electric field creation in a material
19.Place 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
- Oil drops fall under gravity and reach terminal velocity
- A potential difference is applied between the metal plates
- The electric force is adjusted until it balances the gravitational force
- The charge on the drops is determined from the balanced forces
20.Which of the following gives the magnitude of the electric force between the charges?
Medium
- AF = k q² / r²
- BF = k q / r²
- CF = k q² / r
- DF = k q / r
21.The electric force between the charges is repulsive.
Medium
True or false?
22.Match each method of charging with the correct description.
Medium
- Charging by friction
- Charging by electrostatic induction
- Charging by contact
- Earthing
- Electrons are transferred when two insulators are rubbed together
- Charge is separated by a nearby charged object without any physical contact
- Charge is transferred when two objects touch, reducing the potential difference between them
- Connecting a charged body to the Earth so it discharges to 0 V
23.Place the steps for charging a neutral conducting sphere by induction in the correct order.
Medium
- Bring a charged rod near the sphere without touching it
- Ground the sphere so electrons can move onto or away from it
- Remove the earth connection
- Remove the charged rod
24.Which of the following statements about magnetic field lines are correct? (select all that apply)
Medium
- AField lines are directed from the north pole to the south pole outside a magnet
- BThe field is stronger where the field lines are closer together
- CMagnetic field lines can cross each other at neutral points
- DA stationary electric charge produces a magnetic field
- EThe direction of a field line shows the force on a free magnetic north pole placed at that point
25.Which of the following statements about electric field lines are correct? (select all that apply)
Medium
- AThey are directed from positive charges to negative charges
- BThey are equally spaced in a uniform field
- CThey can cross where two fields meet
- DThey are perpendicular to the surface of a charged conducting sphere
- EThe field is weaker where the lines are further apart
26.A positive test charge is placed exactly midway between an electron and a positron that are 150 cm apart. Which of the following statements are correct? (select all that apply)
Hard
- AThe resultant electric field at the midpoint is zero
- BThe resultant force on the test charge at the midpoint is zero
- CThe test charge will remain at rest at the midpoint
- DThe field due to the electron points towards the electron at the midpoint
- EThe field due to the positron points towards the positron at the midpoint
27.A fine mist of oil drops is used in Millikan's experiment rather than water. Why?
Medium
- AOil drops are easier to charge than water drops
- BOil does not evaporate quickly, so the mass of the drops stays constant
- COil drops are attracted to the plates more strongly than water drops
- DOil is a better conductor than water
28.In Millikan's oil drop experiment, a charged oil drop is held stationary between two horizontal metal plates. Which equation correctly relates the forces acting on the drop?
Medium
- AEq = mg
- BEq = mv
- CE/q = mg
- DEq = ma
29.A fine mist of oil drops is sprayed into a chamber in Millikan's experiment. Which of the following is the most likely way the drops become charged as they leave the spray nozzle?
Medium
- ABy friction as they pass out of the nozzle
- BBy gaining protons from the air
- CBy losing neutrons to the air
- DBy electromagnetic induction from the plates
30.A charged oil drop falls under gravity between the plates in Millikan's experiment when there is no electric field. It reaches a terminal velocity. At terminal velocity, which of the following is true?
Medium
- AThe air resistance is zero
- BThe gravitational force equals the air resistance
- CThe gravitational force is greater than the air resistance
- DThe electric force equals the gravitational force
31.In a uniform magnetic field, the field lines are equally spaced parallel lines.
Easy
True or false?
32.A magnetic field is created around a current-carrying wire because of the movement of electrons.
Easy
True or false?
33.The magnetic field lines around a long straight current-carrying wire are circular rings centred on the wire and become further apart with distance from the wire.
Medium
True or false?
34.A free electron enters the space between two parallel charged plates and is deflected as it moves between them. Which of the following best explains the shape of its path?
Medium
- AThe electron experiences a constant force perpendicular to the plates, giving a parabolic path
- BThe electron experiences a force along its direction of motion, giving a straight path
- CThe electron experiences a force that increases with distance, giving an exponential path
- DThe electron experiences no force because it is between the plates
35.A metal sphere of diameter 15 cm is uniformly negatively charged. The electric field strength at its surface is 1.5 × 10⁵ V m⁻¹. Which of the following gives the total surface charge of the sphere? Use k = 8.99 × 10⁹ N m² C⁻².
Medium
- A9.4 × 10⁻⁸ C
- B9.4 × 10⁻⁶ C
- C1.9 × 10⁻⁷ C
- D3.8 × 10⁻⁸ C
36.Four point charges are each placed at a distance d from a point O. Charges B, C and D each have a charge of +q and charge A has a charge of −q. The charges are arranged so that A is opposite C and B is opposite D. What is the magnitude of the resultant electric field strength at O?
Hard
- A2kq/d²
- Bkq/d²
- C4kq/d²
- Dzero
37.A β⁻ particle is placed above a grounded metal plate. Which of the following best describes the electric field lines between the particle and the plate?
Medium
- AThe field lines are directed from the plate to the particle and are perpendicular to the plate at its surface
- BThe field lines are directed from the particle to the plate and are parallel to the plate
- CThe field lines are circular rings centred on the particle
- DThe field lines are directed away from both the particle and the plate
38.An α particle is placed above a grounded metal plate. Compared with a β⁻ particle in the same position, which of the following is true about the electric field created?
Medium
- AThe field lines are in the opposite direction, but the shape of the field is similar
- BThe field lines are in the same direction, but the shape is completely different
- CThe field lines are in the opposite direction and the shape is completely different
- DThe field lines are in the same direction and the shape is the same
39.An α particle and a β⁻ particle are placed near each other in the absence of any other charges. Which of the following statements about the electric field between them is correct?
Medium
- AThere is a point of zero electric field between them, closer to the β⁻ particle
- BThere is a point of zero electric field between them, closer to the α particle
- CThere is no point of zero electric field between them
- DThe resultant electric field is zero everywhere between them
40.A charge −q with mass m orbits a stationary charge +q with a constant orbital radius r. Which of the following gives the orbital speed v of the charge −q?
Medium
- Av = √(kq² / mr)
- Bv = √(kq / mr)
- Cv = kq² / mr
- Dv = √(mr / kq²)
41.Complete the sentence about Millikan's oil drop experiment.
Easy
In Millikan's oil drop experiment, oil is used instead of water because it does not ____ quickly, so the mass of the drops remains constant.
42.Complete the sentence about the right-hand grip rule.
Medium
To find the direction of the magnetic field around a current-carrying wire, point the right-hand thumb in the direction of the ____, and the curled fingers represent the direction of the magnetic field.
43.Two parallel metal plates separated by 3.5 cm have a potential difference of 7.9 kV between them. Calculate the electric force acting on a point charge of 2.6 × 10^-15 C placed between the plates. Give your answer in newtons, to two significant figures.
Medium
44.What is the name of the constant k in Coulomb's law, which has a value of 8.99 × 10⁹ N m² C^-2 in a vacuum?
Medium
45.In Millikan's oil drop experiment, a drop carrying a charge of 4.8 × 10⁻¹⁹ C is held stationary between two horizontal plates separated by 5.0 mm with a potential difference of 300 V. Calculate the mass of the oil drop. Use g = 9.81 N kg⁻¹.
Medium
46.Complete the sentence about the magnetic field around a current-carrying wire.
Medium
The direction of the magnetic field around a current-carrying wire can be found using the ____ rule, and the field lines form ____ rings centred on the wire.
47.Complete the sentence about the magnetic field around a solenoid.
Medium
In a solenoid, the north pole forms at the end where the current flows ____ and the south pole at the end where the current flows ____.
48.What is the name of the rule used to determine the direction of the magnetic field around a current-carrying wire?
Easy
49.What is the name given to the process of removing an outer shell electron from an atom?
Easy
50.Two point charges of +3.0 μC and −3.0 μC are separated by 150 cm in a vacuum. Calculate the magnitude of the electrostatic force between them. Use k = 8.99 × 10⁹ N m² C⁻².
Hard
51.A dust particle of mass 6.7 × 10⁻¹⁵ kg carrying a charge of 2.6 × 10⁻¹⁸ C enters the region between two collecting plates. The electric field strength between the plates is 3.0 × 10⁴ N C⁻¹. Calculate the electrostatic force acting on the particle.
Hard
52.In a simple model of the hydrogen atom, an electron orbits a proton with an electrostatic force of magnitude 5.8 × 10⁻⁹ N. Calculate the orbital radius of the electron. Use k = 8.99 × 10⁹ N m² C⁻² and e = 1.60 × 10⁻¹⁹ C.
Hard
53.State Coulomb's law in words.
Hard
54.Explain how a neutral conducting sphere can become charged by induction using a charged rod.
Medium
55.Explain why the electric field lines around a charged conducting sphere are always perpendicular to its surface, and state what this implies about the electric field inside the sphere.
Hard
56.Explain how the risk of a spark igniting an explosion can be reduced when refuelling an aeroplane.
Medium
57.Explain the shape of the path of a free electron that is incident in the space between two parallel metal plates and is deflected as it moves between them.
Hard
58.Two parallel metal plates separated by 3.5 cm have a potential difference of 7.9 kV between them. Calculate the electric force acting on a point charge of 2.6 × 10^-15 C placed between the plates. Give your answer in newtons, to two significant figures.
Medium
- A2 N
- B-1 N
- C1 N
- D5.9e-10 N
59.In Millikan's oil drop experiment, a drop carrying a charge of 4.8 × 10⁻¹⁹ C is held stationary between two horizontal plates separated by 5.0 mm with a potential difference of 300 V. Calculate the mass of the oil drop. Use g = 9.81 N kg⁻¹.
Medium
- A1 kg
- B2 kg
- C2.9e-15 kg
- D-1 kg
60.Two point charges of +3.0 μC and −3.0 μC are separated by 150 cm in a vacuum. Calculate the magnitude of the electrostatic force between them. Use k = 8.99 × 10⁹ N m² C⁻².
Hard
- A-0.964 N
- B2.036 N
- C0.036 N
- D1.036 N
61.A dust particle of mass 6.7 × 10⁻¹⁵ kg carrying a charge of 2.6 × 10⁻¹⁸ C enters the region between two collecting plates. The electric field strength between the plates is 3.0 × 10⁴ N C⁻¹. Calculate the electrostatic force acting on the particle.
Hard
- A-1 N
- B2 N
- C1 N
- D7.8e-14 N
62.In a simple model of the hydrogen atom, an electron orbits a proton with an electrostatic force of magnitude 5.8 × 10⁻⁹ N. Calculate the orbital radius of the electron. Use k = 8.99 × 10⁹ N m² C⁻² and e = 1.60 × 10⁻¹⁹ C.
Hard
- A2 m
- B6.3e-11 m
- C1 m
- D-1 m

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