Understanding Electric Fields and Field Strength

Electric Fields

• Electric fields are regions of space where a charged particle experiences a force, and are a type of force field.
• Charged particles can be stationary or moving and will experience an electric force in that field.
• All charged particles create their own electric fields.
• Electric fields exert an electrostatic force (FE) on other charged particles that are within the field’s range.

Like charges repel, meaning the electrostatic force on each charge is away from the other charge. Opposite charges attract, meaning the force on each charge is toward the other charge. The size of the force changes with distance.

Electric Field Strength

• Defined as the force per unit charge acting on a positive test charge at a specific point
• Can be calculated using the equation: E = F/Q

Where:

E = electric field strength (N/C) F = electrostatic force on the charge (N) Q = charge (C)

• It is important to use a positive test charge in this definition, as this determines the direction of the electric field.
• Electric field strength is a vector quantity, always directed away from a positive charge and towards a negative charge.

Electric Force between Two Charges

• All charged particles produce an electric field around them.
• This field exerts a force on any other charged particle within range, this is defined by Coulomb's Law.
• 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.
• The equation for the force Fe between two charges with Coulomb's Law is: FE = (Q1Q2) / (4πε₀r²)

FE = electrostatic force between two charges (N) Q₁ and Q2 = two point charges (C) ε₀ = permittivity of free space r = distance between the center of the charges (m)

• The 1/r² relation is called the inverse square law.
• If the separation of two charges doubles, the electrostatic force between them reduces to (1/2)² = 1/4 of its original size.
• ε₀ is a physical constant used to show the capability of a vacuum to permit electric fields.
• If Q₁ and Q2 have opposite charges, then the electrostatic force FE is negative, and attractive between Q₁ and Q2
• If Q₁ and Q2 have the same charge, then the electrostatic force FE is positive, a repulsive force between Q₁ and Q2

Electric Field Due to a Point Charge

• Describes how strong or weak an electric field is at a point.
• A point charge or sphere produces a radial field.
• The electric field strength (E) at a distance (r) due to a point charge (Q) in free space is defined by: E = Q / 4πε₀r²

Where:

Q = point charge producing the radial electric field (C) r = distance from the center of the charge (m) ε₀ = permittivity of free space (F/m)

• The equation shows electric field strength in a radial field isn't constant
• As the distance increases the electric field decreases by a factor of 1/r² (inverse square law)
• When the distanced is doubled, electric field decreases by a factor of 4
• The electric field depends on the charge creating the potential as the distance increases from the center:

If the charge is positive, the potential decreases with distance If the charge is negative, the potential increases with distance This equation is only for the field strength around a point charge (produces a radial field)

• Electric field lines for field strength is a vector

If the charge is positive, the E field strength is positive and points away from the center of the charge If the charge is negative, the E field strength is negative and points towards the center of the charge

Electric Field and Potential

• A positive test charge possesses electric potential energy based on its location within an electric field.
• The magnitude of this electric potential energy relies on both the charge's magnitude and the electric potential value of the field.
• Electric field strength is proportional to the gradient of the electric potential.
• An electric field may be defined by the change in electric potential at different points in the field.
• The potential gradient is defined as the rate of change of electric potential with respect to displacement in the direction of the field.
• Key features of the potential V against distance r graph:

The values for V are all negative/positive for a negative/positive charge As r increases, V against r follows l/r relation for a positive charge and -l/r relation for a negative charge. The gradient of the graph at any particular point is the value of E at that point The graph has a shallow increase (or decrease) as r increases.

Electric Field Between Parallel Plates

• The electric field strength in a uniform field between two charged parallel plates is defined as: E = V/d

Where,

E = electric field strength (Vm⁻¹) V = potential difference between the plates (V) d = separation between the plates (m)

• The electric field strength has units of Vm⁻¹, which are equivalent to the units NC⁻¹.
• Greater voltage is a stronger field.
• Greater separation between the plates is a weaker field.
• *Note - this equation is for electric field strength can't be used to find the electric field strength around a point charge (radial field)
• The direction of the electric field is from the positive terminal of the cell to the negative terminal.

Electric Potential for a Radial Field and Due to a Point Charge

• Positive work is needed to bring a positive test charge closer to another positive charge, therefore potential energy increases.
• The electric potential at a point is defined as the work done per unit charge in bringing a positive test charge from infinity to that point.
• Electric potential is a scalar quantity.
• However, the electric potential can be positive or negative, this is because the electric potential is:

Positive around an isolated positive charg Negative around an isolated negative charge Zero at infinity

• Positive work is done to move a positive test charge from infinity to a point around a positive charge and negative work is done to move it to a point around a negative charge

When a positive test charge moves closer to a negative charge, its electric potential decreases When a positive test charge moves closer to a positive charge, its electric potential increases

• The electric potential in the radial field due to a point charge is defined as: V = Q / 4πε₀r

Where:

V = the electric potential (V) Q = the point charge producing the potential (C) ε₀ = permittivity of free space (F/m) r = distance from the center of the point charge (m)

• For a positive test charge:

As the distance r from the charge Q decreases, the potential V increases (becomes more positive) This is because more work has to be done on the positive test charge to overcome the repulsive force of Q

• For a negative test charge:

As the distance from the charge decreases, the potential V decreases (becomes more negative) This is because less work has to be done on the negative test charge since the attractive force becomes stronger the nearer it gets to Q

• Electric potential varies according to l/r.

Electric field strength varies according to 1/r2.

Representing Radial and Uniform Electric Fields

• Field lines are used to represent the direction and magnitude of an electric field.
• In an electric field, field lines are always directed from the positive charge to the negative charge.
• In a uniform electric field:

the field lines are equally spaced at all points electric field strength is constant at all points in the field the magnitude of the force acting on a test charge is the same at all points in the field

• In a radial electric field:

the field lines are equally spaced as they exit the surface of the charge but the distance between them increases with distance. the electric field strength decreases with distance from the charge producing the field the magnitude of the force acting on a test charge decreases with distance.

• Electric field around a point charge*:

Around a point charge, the electric field is radial and the 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.

• The electric field around a conducting sphere is the same as if all the charge was concentrated at the center

a charged sphere can be treated as a point charge in calculations.

• Electric field lines between two opposite charges are directed from the positive to the negative charge, connect the surfaces of the charges to represent attraction.
• Electric field lines between two like charges are directed away or towards charges.
• When a potential difference is applied between two parallel plates they become charged.
• Electric Field Lines*
• The electric field between two charged parallel plates is directed from the positive to the negative plate.
• A uniform electric field has equally spaced field lines.
• Equipotential Diagrams*
• Equipotential lines (2D) or surfaces (3D) join points that have the same electric potential.
• Always perpendicular to electric field lines
• Represented by dotted lines to show a fixed electric potential
• For a radial equipotential field the are concentric circles around the charge
• The equipotential surface for multiple charges* can be obtained by drawing curves which are perpendicular to the field lines.
• Equipotential lines for a uniform field are evenly spaced parallel lines perpendicular to the field lines.

Explore the concept of electric fields as regions where charged particles experience force. Learn how charged particles create electric fields and exert electrostatic forces on each other, based on charge and distance. Understand electric field strength as force per unit charge, calculated using E = F/Q.