Electric & Magnetic Fields (DP IB Physics)

Millikan's oil drop experiment provides evidence for the quantisation of charge.

The fundamental charge (or elementary charge) is the charge of a single proton (+1.60 × 10⁻¹⁹ C) or electron (-1.60 × 10⁻¹⁹ C).

In Millikan's experiment, oil drops are used as they do not evaporate quickly like water. This allows the mass of the drops to remain constant throughout the experiment.

In Millikan's experiment, the oil drops can become charged by

• friction (using a spray nozzle)

• ionisation (using X-rays)

In Millikan's experiment, when no electric field is applied, the oil drops fall under gravity until they reach a terminal velocity.

In Millikan's experiment, the uniform electric field provides an electric force which is equal and opposite to the gravitational force on an oil drop. The resultant force will then be zero and the drop will become stationary.

In Millikan's experiment, the charge of an oil drop is calculated by equating the gravitational and electric forces

Therefore, the quantities needed to calculate the charge, , are:

• the mass of the drop,

• the potential difference between the metal plates,

• the distance between the metal plates,

The conclusion of Millikan's experiment was:

• the charges of all drops were found to be multiples of the same number (-1.60 × 10⁻¹⁹ C)

• therefore, electric charge must be a quantised quantity

Charging by friction is the transfer of charge (electrons) when two insulating substances move past one another.

One substance gains an excess of positive charge and the other gains an excess of negative charge.

Charging by contact is the transfer of charge (electrons) between two substances when there is physical contact between them.

The excess, or deficit, of electrons, is shared between the two substances.

Charging by induction is the separation of charge caused by the influence of a nearby charged object without any physical contact.

The charged object causes electrons near the surface of the uncharged substance to be either repelled or attracted.

When an uncharged acetate rod is rubbed with an uncharged cloth:

• electrons are transferred from the acetate rod to the cloth by friction

• the cloth becomes negatively charged because it gains electrons

• the acetate rod becomes positively charged because it loses electrons

False.

Earthing a charged body causes it to discharge until it has a potential of 0 V.

A metal sphere can become charged by induction by

• bringing a charged rod near the sphere without touching it (this separates the charges)

• earthing the sphere (this allows electrons to flow to or from the sphere)

• removing the earth connection and the rod (this leaves an excess charge)

False.

A metal sphere can become positively charged by induction by using a negatively charged rod.

When inducing a charge on a metal sphere, its final charge will always be opposite to the rod.

A metal sphere can become charged by contact by

• bringing a charged rod into contact with the sphere (this allows electrons to flow to or from the sphere)

• removing the rod (this leaves an excess charge)

Sparks can occur when

• there is a large build-up of charge on the aircraft

• the potential difference becomes large enough for current to travel through the air

When refuelling an aircraft, the risk of sparking can be reduced by earthing the aircraft and fuel tank to carry excess charge away.

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 electric force between the two identical charges is:

Where:

• = Coulomb constant (8.99 × 10⁹ N m² C^–2)

• = magnitude of the charges (C)

• = separation of the charges (m)

Coulomb's law:

Newton's law of gravitation:

Both electric force and gravitational force follow an inverse square law with distance.

The electric force between two opposite charges is negative.

A negative force means the force is attractive.

The electric force between two similar charges is positive.

A positive force means the force is repulsive.

False.

Coulomb's law can only be applied to charged spheres.

False.

The value of, , (Coulomb constant) is not the same in all materials.

• In a vacuum (or air):

• In other materials:

Where = permittivity of free space and = permittivity of a material

The permittivity of a medium represents the medium's ability to transfer an electric field and force between charges in it.

The permittivity of a medium is related to the permittivity of free space by:

Where:

• = relative permittivity

• = permittivity of a medium

• = permittivity of free space

True.

All materials have a higher relative permittivity than air.

• Relative permittivity of air:

• Relative permittivity of other materials:

The electric field strength at a point is the force per unit charge experienced by a small positive test charge placed at that point.

The two equivalent units of electric field strength are N C^-1 and V m^-1.

Test charges are used to define the strength of a field at a point and the direction a charge will move in the field.

This is because electric field strength is a vector quantity.

The direction of an electric field is defined by the direction of the force that acts on a positive test charge, such that

• the force on a positive charge is in the direction of the field

• the force on a negative charge is in the opposite direction

The electric field strength due to a point charge is:

Where:

• = Coulomb constant (8.99 × 10⁹ N m² C^–2)

• = magnitude of the charge (C)

• = distance from the charge to the point (m)

False.

The variation of electric field strength around the outside of a charged sphere and a point charge are identical.

Inside the charged sphere, the electric field strength is zero.

The resultant electric field due to multiple charges is determined by vector addition. This could be

• using simple addition (if the point lies on a line joining the charges)

• using Pythagoras (if the point makes a right-angled triangle with the charges)

A uniform electric field can be set up between two parallel metal plates by connecting them to the terminals of a power supply.

The strength of an electric field between two parallel plates is:

Where:

• = potential difference between the plates (V)

• = separation of the plates (m)

The electron will move to the left towards the positively charged plate.

Electric field lines represent

• the strength of the electric field

• the direction of the electric field

The electric field lines around a positive point charge are

The electric field lines around a negative point charge are

The electric field lines around two opposite charges are

The electric field lines around two similar charges are

The electric field lines between a positive charge and an earthed plate are

The grounded plate has a potential of 0 V, so the field lines are directed from the positive charge to the 'less positive' plate.

True.

Field lines are always perpendicular to the surface of a conducting sphere.

False.

The field lines around the edges of two parallel plates are not uniform.

The strength of a radial electric field depends on

• the magnitude of the charge producing the field

• the distance between the charge and a point

The density of field lines represents the strength of an electric field

• the closer together the field lines, the stronger the field

• the further apart the field lines, the weaker the field

False.

Magnetic fields are produced around all moving charges.

The electric potential at a point is the work done per unit charge in taking a small positive test charge from infinity to a defined point.

The magnetic flux density of a field is the number of magnetic field lines passing through a region of space per unit area.

False.

Electric potential is a scalar quantity.

One tesla (T) 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.

The unit of electric potential is J C^-1 or V.

The flux density is a measure of the strength of a magnetic field

• the higher the flux density, the stronger the magnetic field

• the lower the flux density, the weaker the magnetic field

The electric potential due to a point charge is:

Where:

• = Coulomb constant (8.99 × 10⁹ N m² C^–2)

• = magnitude of the charge (C)

• = distance from the charge to the point (m)

A uniform magnetic field can be set up between two flat permanent magnets when the north pole of one magnet is parallel to the south pole of the other.

True.

Electric potential increases when a test charge moves closer to an isolated positive charge.

The right-hand grip rule is used to determine the direction of a magnetic field around a current:

• the thumb points in the direction of the current

• the fingers curl in the direction of the magnetic field

False.

Electric potential increases when a test charge moves away from an isolated negative charge.

The magnetic field lines around a current-carrying wire:

For a positive charge, electric potential decreases as the distance increases.

The magnetic field lines around a solenoid:

False.

Electric potential decreases in the direction of electric field lines.

The magnetic field lines around a flat circular coil:

False.

Inside a charged sphere, the electric potential has a constant non-zero value.

False.

When viewed from the end of a solenoid, the pole is a south pole if the current travels clockwise around the coil.

False.

The combined electric potential at a point due to multiple charges is determined by adding together the potentials due to each of the charges.

Electric potential energy is the work done when bringing all the charges in a system to their positions from infinity.

False.

Electric potential energy can be positive or negative depending on the signs of the charges involved.

The electric potential energy of two similar charges decreases as the separation between them increases.

The electric potential energy of two opposite charges increases as the separation between them increases.

The electric potential energy of two opposite charges is:

Where:

• = Coulomb constant (8.99 × 10⁹ N m² C^–2)

• = magnitude of the charges (C)

• = separation between charges (m)

True.

Electric potential and electric potential energy are both equal to zero at infinity.

The change in electric potential energy (or work done) is

Where:

• = Coulomb constant (8.99 × 10⁹ N m² C^–2)

• , = magnitudes of the charges (C)

• = initial separation between charges (m)

• = final separation between charges (m)

The area under a force-distance graph represents the change in electric potential energy or the work done in moving the charge from one point to another.

When a small mass moves away from a large mass, the gravitational potential energy increases.

The change in electric potential energy is similar when:

• a small positive charge moves away from a large negative charge

• a small positive charge moves towards a large positive charge

When a small mass moves towards a large mass, the gravitational potential energy decreases.

The change in electric potential energy is similar when:

• a small positive charge moves towards a large negative charge

• a small positive charge moves away from a large positive charge

The work done in moving a charge, , in an electric field is:

Where:

• = magnitude of charge moving in the field (C)

• = potential difference between two points (V or J C⁻¹)

Electric potential difference is the difference in electric potential between two points.

It is equal to the work done when a charge of 1 C is moved between the points.

The potential difference due to a point charge is:

Where:

• = Coulomb constant (8.99 × 10⁹ N m² C^–2)

• = magnitude of charge producing the potential (C)

• = initial distance from charge Q (m)

• = final distance from charge Q (m)

Potential gradient is the rate of change of electric potential with respect to displacement in the direction of the field.

In the potential gradient equation

The negative sign indicates that the direction of the field strength opposes the direction of increasing potential.

The gradient of a potential-distance graph represents the electric field strength at that point.

The area under a field-distance graph represents the potential difference between the two points.

False.

The potential-distance graph for a positive charge follows a relation.

All values of potential are positive for a positive charge.

False.

The field-distance graph for a negative charge follows a (inverse square law) relation.

All values of field strength are negative for a negative charge

True.

The curve of an graph is steeper than its corresponding graph.

This is because graphs follow a relation whereas graphs follow a relation.

Equipotential surfaces (or lines) connect points of equal electric potential.

False.

Equipotential lines are always perpendicular to electric field lines.

True.

No work is done as a charge moves along an equipotential line.

The key features of the equipotential lines in a radial electric field are:

• concentric circles

• become further apart with distance

The key features of the equipotential lines in a uniform electric field are:

• horizontal straight lines

• parallel

• equally spaced

The field lines (black arrows) and equipotential lines (dotted green lines) for a positive and negative point charge are:

The field lines (black arrows) and equipotential lines (dotted green lines) for a uniform electric field are:

This is the equipotential surface for two opposite charges. The central line has a potential of 0 V.

This is the equipotential surface for two similar charges. The region of empty space in the centre indicates where the resultant field is zero.

Equipotential lines represent the potential gradient, so the sign of a charge can be identified by looking for

• positive potentials which decrease with distance represent a positive charge

• negative potentials which increase with distance represent a negative charge