Chapter 7 Electric Fields

Question 1

Electric Field Definition

Answer 1

• An electric field is a region of space in which an electric charge “feels” a force
• Electric field strength at a point is defined as:
• *The electrostatic force per unit positive charge acting on a stationary point charge at that point**

Question 2

• Electric field strength can be calculated using the equation:

Answer 2

• Where:
  
  • E = electric field strength (N C^-1)
  • F = electrostatic force on the charge (N)
  • Q = charge (C)

Question 3

The electric field strength is a vector quantity, it is always directed:

Answer 3

• Away from a positive charge
• Towards a negative charge
• Recall that opposite charges (positive and negative) charges attract each other
• Conversely, like charges (positive and positive or negative and negative) repel each other

Question 4

• The electric field strength equation can be rearranged for the force F on a charge Q in an electric field E:

Answer 4

F = QE

• Where:
  
  • F = electrostatic force on the charge (N)
  • Q = charge (C)
  • E = electric field strength (N C^-1)

Question 5

The direction of the force is determined by the charge:

Answer 5

• If the charge is positive (+) the force is in the same direction as the E field
• If the charge is negative (-) the force is in the opposite direction to the E field
• The force on the charge will cause the charged particle to accelerate if its in the same direction as the E field, or decelerate if in the opposite
• Note: the force will always be parallel to the electric field lines

Question 6

An electric field strength E exerts a force F on a charge +Q in a uniform electric field

Answer 6

Question 7

Point Charge Approximation

Answer 7

• For a point outside a spherical conductor, the charge of the sphere may be considered to be a point charge at its centre
  
  • A uniform spherical conductor is one where its charge is distributed evenly
• The electric field lines around a spherical conductor are therefore identical to those around a point charge

Question 8

a spherical conductor is a

Answer 8

• charged sphere
• The field lines are radial and their direction depends on the charge of the sphere
  
  • If the spherical conductor is positively charged, the field lines are directed away from the centre of the sphere
  • If the spherical conductor is negatively charged, the field lines are directed towards the centre of the sphere

Question 9

• The direction of electric fields is represented by electric field lines

Answer 9

• Electric field lines are directed from positive to negative
  
  • Therefore, the field lines must be pointed away from the positive charge and towards the negative charge
• A radial field spreads uniformly to or from the charge in all directions
  
  • e.g. the field around a point charge or sphere
• Around a point charge, the electric field lines are directly radially inwards or outwards:
  
  • If the charge is positive (+), the field lines are radially outwards
  • If the charge is negative (-), the field lines are radially inwards

Question 10

A uniform electric field has the same

Answer 10

• electric field strength throughout the field
  
  • For example, the field between oppositely charged parallel plates
• This is represented by equally spaced field lines
  
  • This shares many similarities to uniform gravitational field lines on the surface of a planet

Question 11

A non-uniform electric field has

Answer 11

• varying electric field strength throughout
• The strength of an electric field is determined by the spacing of the field lines:
  
  • A stronger field is represented by the field lines closer together
  • A weaker field is represented by the field lines further apart

Question 12

The electric field between two parallel plates is directed from the positive to the negative plate. A uniform E field has equally spaced field lines

Answer 12

• The electric field lines are directed from the positive to the negative plate

Question 13

Electric field lines around point charges are

Answer 13

• radially outwards for positive charges and radially inwards for negative charges
• The field lines must be drawn with arrows from the positive charge to the negative charge

Question 14

• The electric field strength of a uniform field between two charged parallel plates is defined as:

Answer 14

• Where:
  
  • E = electric field strength (V m^-1)
  • ΔV = potential difference between the plates (V)
  • Δd = separation between the plates (m)
• Note: the electric field strength is now also defined by the units V m^-1

Question 15

Electric Field Strength Equation shows

Answer 15

• The greater the voltage between the plates, the stronger the field
• The greater the separation between the plates, the weaker the field
• Remember this equation cannot be used to find the electric field strength around a point charge (since this would be a radial field)
• The direction of the electric field is from the plate connected to the positive terminal of the cell to the plate connected to the negative terminal

Question 16

The E field strength between two charged parallel plates is the ratio of the potential difference and separation of the plates

Answer 16

• Note: if one of the parallel plates is earthed, it has a voltage of 0 V

Question 17

Electric Field of a Point Charge

Answer 17

• The electric field strength at a point describes how strong or weak an electric field is at that point
• The electric field strength E at a distance r due to a point charge Q in free space is defined by:

Question 18

This equation shows:

Answer 18

• Electric field strength is not constant
• As the distance from the charge r increases, E decreases by a factor of 1/r²
• This is an inverse square law relationship with distance
• This means the field strength decreases by a factor of four when the distance is doubled
• Note: this equation is only for the field strength around a point charge since it produces a radial field

Question 19

The electric field strength is a (scaler or vector?)

Answer 19

• vector Its direction is the same as the electric field lines
  
  • If the charge is negative, the E field strength is negative and points towards the centre of the charge
  • If the charge is positive, the E field strength is positive and points away from the centre of the charge
• This equation is analogous to the gravitational field strength around a point mass

Question 20

Motion of Charged Particles

Answer 20

• A charged particle in an electric field will experience a force on it that will cause it to move
• If a charged particle remains still in a uniform electric field, it will move parallel to the electric field lines (along or against the field lines depending on its charge)
• If a charged particle is in motion through a uniform electric field (e.g. between two charged parallel plates), it will experience a constant electric force and travel in a parabolic trajectory

Question 21

The parabolic path of charged particles in a uniform electric field

Answer 21

Question 22

The direction of the parabola will depend on the charge of the particle

Answer 22

• A positive charge will be deflected towards the negative plate
• A negative charge will be deflected towards the positive plate
• The force on the particle is the same at all points and is always in the same direction
• Note: an uncharged particle, such as a neutron experiences no force in an electric field and will therefore travel straight through the plates undeflected

Question 23

The amount of deflection depends on the following properties of the particles:

Answer 23

• Mass – the greater the mass, the smaller the deflection and vice versa
• Charge – the greater the magnitude of the charge of the particle, the greater the deflection and vice versa
• Speed – the greater the speed of the particle, the smaller the deflection and vice versa

Question 24

All charged particles produce an

Answer 24

electric field around it

• This field exerts a force on any other charged particle within range

Question 25

The electrostatic force between two charges is defined by

Answer 25

• Coulomb’s Law
  
  • Recall that the charge of a uniform spherical conductor can be considered as a point charge at its centre
• Coulomb’s Law states that:

The electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation

Question 26

• The Coulomb equation is defined as:

Answer 26

• Where:
  
  • F_E = electrostatic force between two charges (N)
  • Q₁ and Q₂ = two point charges (C)
  • ε₀ = permittivity of free space
  • r = distance between the centre of the charges (m)

Question 27

inverse square law of the electrostatic force

Answer 27

• The 1/r² relation is called the inverse square law
  
  • This means that when a charge is twice as far as away from another, the electrostatic force between them reduces by (½)² = ¼
• If there is a positive and negative charge, then the electrostatic force is negative, this can be interpreted as an attractive force
• If the charges are the same, the electrostatic force is positive, this can be interpreted as a repulsive force
• Since uniformly charged spheres can be considered as point charges, Coulomb’s law can be applied to find the electrostatic force between them as long as the separation is taken from the centre of both spheres

Question 28

• The electric potential at a point is defined as:

Answer 28

The work done per unit positive charge in bringing a small test charge from infinity to a defined point

• Electric potential is a scalar quantity
  
  • This means it doesn’t have a direction
• However, you will still see the electric potential with a positive or negative sign. This is because the electric potential is:
  
  • Positive when near an isolated positive charge
  • Negative when near an isolated negative charges
  • Zero at infinity

Question 29

In order to move a positive charge closer to another positive charge

what must be done?

Answer 29

• work must be done to overcome the force of repulsion between them
• Energy is therefore transferred to the charge that is being pushed upon
  
  • This means its potential energy increases

Question 30

Positive work is done by the mass from infinity to a point around a positive charge and negative work is done around a negative charge. This means:

Answer 30

• • When a test charge moves closer to a negative charge, its electric potential decreases
    
    • When a test charge moves closer to a positive charge, its electric potential increases
• To find the potential at a point caused by multiple charges, add up each potential separately

Question 31

• The electric potential in the field due to a point charge is defined as:

Answer 31

• Where:
  
  • V = the electric potential (V)
  • Q = the point charge producing the potential (C)
  • ε₀ = permittivity of free space (F m^-1)
  • r = distance from the centre of the point charge (m)

Question 32

This equation shows that for a positive (+) charge:

Answer 32

• As the distance from the charge r decreases, the potential V increases
• This is because more work has to be done on a positive test charge to overcome the repulsive force

Question 33

For a negative (−) charge:

Answer 33

• As the distance from the charge r decreases, the potential V decreases
• This is because less work has to be done on a positive test charge since the attractive force will make it easier

Question 34

The potential changes as an inverse law with distance near a charged sphere

Answer 34

• Note: this equation still applies to a conducting sphere. The charge on the sphere is treated as if it concentrated at a point in the sphere from the point charge approximation

Question 35

The potential changes as an inverse law with distance near a charged sphere

Answer 35

• included in the charge
• The electric potential changes according to an inverse square law with distance

Question 36

• An electric field can be defined in terms of the variation of electric potential at different points in the field:

Answer 36

The electric field at a particular point is equal to the negative gradient of a potential-distance graph at that point

• The potential gradient is defined by the equipotential lines
  
  • These demonstrate the electric potential in an electric field and are always drawn perpendicular to the field lines

Question 37

Equipotential lines around a radial field or uniform field are perpendicular to the electric field lines

Answer 37

Question 38

Equipotential lines are lines of equal electric potential

Answer 38

• Around a radial field, the equipotential lines are represented by concentric circles around the charge with increasing radius
• The equipotential lines become further away from each other
• In a uniform electric field, the equipotential lines are equally spaced

Question 39

• The potential gradient in an electric field is defined as:

Answer 39

The rate of change of electric potential with respect to displacement in the direction of the field

Question 40

• The electric field strength is equivalent to this, except with a negative sign:

Answer 40

• Where:
  
  • E = electric field strength (V m^-1)
  • ΔV = change in potential (V)
  • Δr = displacement in the direction of the field (m)
• The minus sign is important to obtain an attractive field around a negative charge and repulsive field around a positive charge

Question 41

The electric potential around a positive charge decreases with distance and increases with distance around a negative charge

Answer 41

Question 42

The electric potential changes according to the charge creating the potential as the distance r increases from the centre:

Answer 42

• • If the charge is positive, the potential decreases with distance
    
    • If the charge is negative, the potential increases with distance
• This is because the test charge is positive

Question 43

• The electric potential energy E_p at point in an electric field is defined as:

Answer 43

The work done in bringing a charge from infinity to that point

Question 44

• The electric potential energy of a pair of point charges Q₁and Q₂ is defined by:

Answer 44

Question 45

The potential energy equation is defined by

Answer 45

• the work done in moving point charge Q₂ from infinity towards a point charge Q₁.

Question 46

• The work done is equal to:

Answer 46

W = VQ

• Where:
  
  • W = work done (J)
  • V = electric potential due to a point charge (V)
  • Q = Charge producing the potential (C)
• This equation is relevant to calculate the work done due on a charge in a uniform field
• Unlike the electric potential, the potential energy will always be positive
• Recall that at infinity, V = 0 therefore E_p = 0
• It is more useful to find the change in potential energy eg. as one charge moves away from another

Question 47

The change in potential energy from a charge Q₁ at a distance r₁ from the centre of charge Q₂ to a distance r₂ is equal to:

Answer 47

ΔE_p= Q₁Q₂/4πE₀(1/r₁ -1/r₂)

• The change in electric potential ΔV is the same, without the charge Q₂

ΔV= Q/4πE₀(1/r₁ -1/r₂)

• Both equations are very similar to the change in gravitational potential between two points near a point mass