Unit D2: Electricity and magnetism

The gold leaf electroscope

The gold leaf electroscope

Where do the charges come from?

​

Conservation of:

• Energy
• Momentum
• Charge
• Lepton number
• Baryon number

What is happening?

Attaching a copper earthing wire to plane before refueling

Dangers

Dangers

Why are these surgeons wearing copper bands on their wrists?

There are 6 main points to make here.

Dangers

Why are these surgeons wearing copper bands?

There are 6 main points to make here.

1. The charge is due to movement of electrons
2. The electron movement is between two insulators
3. The electrons are transferred from one material to the other by friction
4. The electrons gather on one insulator but cannot escape – static
5. The charge could build up to dangerous levels, perhaps escaping down a metal implement (for example a scalpel)
6. The copper bracelet allows any electrons that start to gather somewhere to go, preventing a build-up of charge

Dangers

Dangers

Electric field

An area or region where a charge feels a force is called an electric field.

​

The electric field strength at any point in space is defined as the force per unit charge (on a small positive test charge) at that point.

​

E = F/q (in N C^-1)

Electric field patterns

A field is a region of space where small positive test mass/charge feels a force

An electrical field is a region of space in which a small positive test charge experiences a force

Electric field patterns

The arrows show the direction of force that would be felt by a positive charge in the field

Electric field patterns

An electrical field is a region of space in which a small positive test charge experiences a force

Note: The direction of a field line in the electric field is the direction of the force on a small positive test charge.

(or from positive to negative if that is easier)

​

​

​

Shuttling Ball Experiment

Force

Coulomb found that the force between two point charges is proportional to the product of the two charges

​

​

and inversely proportional to the square of the

distance (r) between the charges

​

Example

• A small cork with an excess charge of +7.0 µC is placed 14 cm from another cork, which carries a charge of −3.2 µC. What is the magnitude of the electric force between the corks?

k = 8.99 × 10⁹ N m² C^-2

Elementary Charge = 1.60 × 10^-19 C

How many electrons?

• A small cork with an excess charge of +7.0 µC is placed 14 cm from another cork, which carries a charge of −3.2 µC. What is the magnitude of the electric force between the corks?

k = 8.99 × 10⁹ N m² C^-2

Elementary Charge = 1.60 × 10^-19 C

• How many excess electrons on the second cork??

Coulomb’s law

​

​

The constant k is sometimes written as

​

​

​

where ε_o is called the permittivity of free space.

​

Permittivity

Permittivity changes relative to the substance

Relative Permittivity

IB might ask you about this: the higher the relative permittivity, the harder it is for electrostatic forces to travel over a distance…

Some examples of relative permittivities:

Permittivity

Sample question including ε₀

A point charge of 4.5 × 10⁻⁸ C is situated in air 3.2 cm from another charge of –1.3 × 10⁻⁷ C.

a Determine the electrical force between them.

b If they were separated by polythene, calculate the approximate force between the charges.

​

Sample question including ε₀

A point charge of 4.5 × 10⁻⁸ C is situated in air 3.2 cm from another charge of –1.3 × 10⁻⁷ C.

a Determine the electrical force between them.

b If they were separated by polythene, calculate the approximate force between the charges.

Answer

a F = –5.1 × 10^–2 N

The negative sign represents an attractive force.

b Polythene has a relative permittivity of about 2, so the force would be divided by 2 (approximately), F ≈ −3 × 10⁻² N.

​

Summary so far:

What is the force between two charges of 3.2 μC and 5.6 μC separated by a distance of 34 cm?

Using the relationships

What is the force between two charges of 3.2 μC and 5.6 μC separated by a distance of 34 cm?

Using the relationships

What is the force between two charges of 3.2 μC and 5.6 μC separated by a distance of 34 cm?

F = 1.4 N

Using the relationships

What is the force experienced by a charge of +6.3 μC placed at a point where the electric field strength is 410 NC^-1?

Using the relationships

What is the force experienced by a charge of +6.3 μC placed at a point where the electric field strength is 410 NC^-1?

Using the relationships

What happens if A is negative?

​

Try drawing this.

Combining charges and fields

Combining charges and fields

Electric field

Electric field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one charge) must use vector addition.

Field here due to both charges?

q₁

q₂

Electric field

Electric field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one charge) must use vector addition.

Field here due to both charges?

Field due to q₁

q₁

q₂

Electric field

Electric field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one charge) must use vector addition.

q₁

q₂

Resultant field

Field due to q₁

Field due to q₂

Combining charges and fields

Combining charges and fields

Charge is a scalar quantity, with the unit of C (Coulomb)

​

Coulomb’s Law cf Newton’s Gravitational law

​

​

Electric field strength cf gravitational field strength

​

​

Can you write electric field strength in terms of k, q and r?

​

Charge, a recap

Parallel

​

At right angles to the plates

​

Pointing from positive to negative (direction a positive test charge would travel)

Parallel plates and an electric field

If you move a test charge between the plates then work must be done:

W = Fd = Eq x d

Can you recall the definition of Potential Difference?

Energy in a uniform field

If you move a test charge between the plates then work must be done:

W = Fd = Eqd

Can you recall the definition of Potential Difference?

Work done per unit charge to move across a PD of V

Energy in a uniform field

Substitution and rearranging gives the field strength at any point between two plates, that are separated by a distance d

W = Fd = Eqd and V = W/q

​

Energy in a uniform field

The electric field strength E is the force per unit charge on a test charge placed at that point in the field (NC^-1)

The formula for calculating the field strength between two parallel plates of separation d is:

Summary

Gravitational potential energy

Gravitational potential energy at a point is defined as the work done to move a mass from infinity to that point.

​

​

​

​

E_p is always negative

Electrical potential energy

Electrical potential energy at a point is defined as the work done to move a positive charge from infinity to that point.

​

​

​

Electrical Potential

The Electrical potential at a point is the work done per unit charge on a small positive test charge moving from infinity to that point. It is given by

​

​

Note the difference between electrical potential energy (J) and Electrical potential (J.C^-1)

1. What is the potential difference (pd) between A and C?
2. What is the pd between B and D?
3. If a charge of +3 C was placed at B, how much PE would it have?
4. If a charge of +2 C was moved from C to B, how much work would be done?
5. If a charge of –2 C moved from A to B, how much work would be done?
6. If a charge of +3 C was placed at B and released

(a) what would happen to it?

(b) how much KE would it gain when it reached A?

• If an electron was released at A and accelerated to B how much KE would it gain in eV?
• If an electron was taken from C to D how much work would be done in eV?

​

Questions

This also defines an extremely important unit: the electronvolt

​

1eV = the energy one electron gains moving through a potential difference of 1V

​

​

W (J) = W (eV) x 1.6 x 10^-19

Electron volts (as an aside)

Field and equipotentials

Equipotentials are always perpendicular to field lines. Diagrams of equipotential lines give us information about the gravitational field in much the same way as contour maps give us information about geographical heights.

Equipotential surfaces/lines

Field strength = gradient on a potential vs distance graph

Summary so far: