ELECTRIC FIELD STRENGTH

UNIT OF ELECTRIC FIELD STRENGTH

POSITIVE TEST CHARGES AT A CERTAIN POIN IN THE ELECTRIC FIELD

It will be acted by a force - F - due to the electric field. The electric field strength is then given the equation

electric field strength = force / charge

E = F / Q

ELECTRIC FIELD STRENGTH NOTES

Electric field strength is a vector, it is in the direction of the force on a positive test charge. So the direction of field lines at any point is the same as the direction of the electrical field strength at that point.

Force = Same direction as electric field if positive charge

Opposite direction to field if negative charge

The test charge must be less than 1 coulomb so it doesn't alter the electric field strength

LIGHTNING CONDUCTOR

Metal rod at the top of a tall building. It's connected to the ground by a metal conductor which is very thick. When a charged cloud is overheated, a strong electric field is created near the conductor which ionises the air molecules. These ionised air molecules discharge the cloud which reduces the risk of lightning.

*Air is an insulator and is ionised by strong electric fields which pull elctrons out othe air molecules.

ELECTRIC FIELD BETWEEN TWO PARALLEL PLATES*

ELECTRIC FIELD STRENGTH USING VOLTAGE

Electric field strength can be calculated using potential difference;

electric field strength = voltage / distance(seperation) between the two plates

E = V / d

This unit is Vm^-1

PROVING E = V / d (1)

The force - F - on a test charge - Q -

 Force = Charge x Electric field strength

F = QE

If charge - Q - is moved from positive plate to negative; work is done to move it. The field does this work on Q.

Work done = force x distance moved

W = Fd

PROVING E = V / d (2)

The definition of potential difference - V - is the work done per unit charge when a small charge is moved through it.

Voltage = Work done / Charge

V = W / Q

Work done = Charge x Electric field strength x distance

W = QEd

PROVING E = V / D

 This means that:

Voltage = (Charge x Electric field strength x distance) / Charge

V = QEd / Q

The charges appear on both sides of the divide sign so they cancel out

V = Ed  so E = V / d

FIELD FACTORS

Electric fields are near any charged object or body. The greater the charge, the stronger the electric field.

- Charged metal conductors have thier charge spread across the surface, the more conecntrated the charge is, the greater the strength of the electric field

ELECTRIC FIELD PATTERN BETWEEN A V-SHAPED CONDUCTOR AND FLAT PLATE: *

ELECTRIC FIELD BETWEEN TWO OPPOSITELY CHARGED PARALLEL PLATES

This depends on the concentration of charge on the surface of the plates. The charge on each plate is spread evenly across the surface of the plate facing the other plate

The elctrical field strength is proportional to the charge per unit area

E ≈ Q / A

STATIC ELECTRICITY

ELECTRONS

Electrons charge in most situations. Uncharged atoms contain equal numbers of protons and electrons. ADDING electrons, negatively charges the atom, REMOVING electrons positively charges the atom.

e.g when a perspex rod is rubbed with a dry cloth, the electrons from the rod transfer to the cloth. This removes electrons from the rod making it positive and adds electrons to the cloth making it negative

ELECTRIC CONDUCTORS

EARTHING

INSULATING MATERIALS

THE SHUTTLING BALL EXPERIMENT

Shows elecric current is a flow of charge

Conducting ball is hung by insulating thread between two vertical plates of opposite charge

When high voltage is applied, the ball bounces back and forth between the two plates

Everytime it touches the negative plates, electrons are transferred to the ball (so it's negatively charged) and repelled by the negative plate yet attracted by the positive plate. Here electrons transfer to the positive plate and the ball becomes positive and repelled again

CURRENT CHARGE AND FREQUENCY

Current = Charge x Frequency 

I = Qf 

Frequency = 1 / time 

Therefore current = charge / time for one cycle

I = Q/Time for one cycle

GOLD LEAF ELECTROSCOPE

Used to detect charge 

If charged obejct is in contact with metal cap of electroscope, some charge transfers to electroscope which then flows to the gold leaf and metal stem causing them both to have the same charge so they repel each other. The leaf is light so as being repelled by the metal stem, it rises. If another object with the same charge is bought close too, this will cause the leaf to rise further as more charge is forced to transfer to the leaf and stem

CHIPS 

The small amount of charge on pins of a microchip is enough to destroy the circuits inside a chip. 

If the pins are touched by a charged near a charged object, they will be earthed. This means the electrons will transfer from the pins to the earth.

Microchips are stored in antistatic packets which allow charges to flow across the surface 

FIELD LINES

Any two objects exert equal and opposite forces; 

Electric fields surround each charge

If a small positive test charge is placed near an object with a much bigger charge that is also positive, the test charge will follow a path AWAY from the big charge. The path is called field lines

FIELD LINES OF 2 OPPOSITELY CHARGED POINTS*

FIELD LINES OF A POINT NEAR A PLATE*

FIELD LINES OF TWO OPPOSITELY CHARGED PLATES*

OPPOSTIELY CHARGED POINTS

POINT OBJECT NEAR AN OPPOSITELY CHARGED FLAT PLATE

TWO OPPOSITELY CHARGED PLATES

THE VAN DE GRAAF GENERATOR

Produces sparks in the air

Charge created when a rubber belt rubs against a metal pad and is carried up the belt to the metal dome. As charge increases on the ome, the pd between the dome and earth increases until sparking occurs. 

Sparks transfer energy from the dome. Work is done to charge the dome because a force is needed to move the charge on the belt up to the dome. Electric potential energy of the dome increases as it charges up. Some of this energy is transferred from the dome when a spark is created

TWO OBJECTS OF THE SAME CHARGE

CONSIDERING TWO CHARGED OBJECTS OF THE SAME CHARGE

ELECTRIC POTENTIAL AT A CERTAIN POSITION IN ANY ELECTRIC FIELD

ZERO POTENTIAL ENERGY

UNIT OF ELECTRICAL POTENTIAL

THE RELATIONSHIP BETWEEN ELECTRIC POTENTIAL ENERGY (E_p) AND ELECTRIC POTENTIAL (V)

Electric potential = electric potential energy / charge

V = E_P/Q

So 

E_P = QV

EQUIPOTENTIALS

Lines of constant potential

Test charges moving along an equipotential has constant potential energy.

No work is done by the electric field because the force due to the field is at right angles to the equipotential -- lines of force of the electric field cross the equipotential lines at right angles

POTENTIAL GRADIENTS

POTENTIAL GRADIENT OF A NON - UNIFORM FIELD

POTENTIAL GRADIENTS IN A UNIFORM FIELD 

ELECTRIC POTENTIAL GRADIENT FACTS

The potential(negative) is proportional to the distance

The potential gradient is constant

The potential gradient increase in the opposite direction to the electric field

The potential gradient = electric potential / distance

= V / d

ELECTRIC FIELD STRENGTH AND POTENTIAL GRADIENT

COULOMB'S LAW  - LINK OF F AND r

The force is proportional to 1 / radius squared

From here Coulomb law states that:

Force = Constant of proportionality x Charge of one object x charge of second object / distance between them squared

Constant of proportionality = 1 / 4πε_ο

F = Q₁Q₂ / r²

SALT CRYSTALS DISSOLVING IN WATER 

Salt crystals are ionic

Sodium ions and chlorine ions are oppositely charged

Electrostatic forces between them hold them together

Water weakens the electrostatic forces between the ions at the surface so they break free from the surface of the crystals, so they dissolve

The force in water is 80 x weaker than if the crystals were in air

COULOMBS LAW APPLIED TO THE FORCE ON A TEST CHARGE (q)

Force = Constant of proportionality x point charge x test charge / distance sqaured

F = kQq / r² 

Electric field strength at distance (r) = Force / test charge = constant of proportionality x point charge / distance squared

E = F / Q = kQ / r² 

POINT CHARGES

TEST CHARGES IN A FIELD

POSITIVE POINT CHARGE AND POSITIVE TEST CHARGE

Field lines radiate away from point charge because the test charge in the field experiences a force directly away from the point charge wherever it's placed. 

Coulombs law states that force = (one / four x pi x epsilon) x (point charge x test charge / distance squared)

F = (1/4πεο) Qq/r²

Electric field strength = force / test charge

so electric field strength = point charge / 4,pi,epsilon x distance²

E = Q / 4πεο x r²

WHAT IF THE POINT CHARGE IS NEGATIVE

If the point charge is negative using the formula; E = 4πεο x r², the value of E will be negative so the field lines will 

point towards the point charge

ELECTRIC FIELD STRENGTH AS A VECTOR

If a test charge is in an electric field with 2 or more point charges, each charge exerts a force on the test charge. 

The resultant force on the test charge gives the resultant electric field strength at the test charge

FORCES IN THE SAME DIRECTION

For example a positive test charge between a negative point charge and positive point charge have forces in the same direction because the positive point charge repels the test charge and the negative point charge attracts the point charge

This means the resultant force is equal to the sum of both forces 

F = F₁ + F₂ 

RESULTANT ELECTRIC FIELD STRENGTH FOR FORCES IN THE SAME DIRECTION

Force = electric field strength x charge

F = qE

Rearranging this gives electric field strength = force / charge

E= F/q

 Resultant force = force from negative + force from positive 

F = F₁ + F₂

So resultant electrical field strength is equal to (charge x electric field strength1 + charge x electric field strength 2) / charge 

E = (qE₁ + qE₂) / q

Charge,q, cancels out to leave E = E₁ + E₂

FORCES IN OPPOSITE DIRECTIONS

A test charge between two positive point charges. The forces will be in opposite direction because the forces repel each other so the resultant force = 

F = F₁ - F₂ 

Electrical field strength  

E = E₁ - E₂

FORCES AT RIGHT ANGLES TO EACH OTHER

Pythagoras theorum

F² = F₁² + F₂²

Electric field strength 

E² = E₁² + E₂²

MORE ON RADIAL FIELDS

Electric field lines of force surrounding a point charge are radial - the equipotentials are circles around the point charge

THE ELECTRIC FIELD STRENGTH EQUATION 

E = Q/4πεο r²

Shows that the electric field strength is inversely proportional

to the square of the distance. This is an inverse square law, 

so shows a curve on a graph because 

Electric field strength is proportional to1/r²

NEGATIVES

Negative electric field strength means that the field is acting towards a negative charge

Negative electric potential means a value below zero

*E varies more sharply with distance than V

I 

Q

e

CHARGE OF ELECTRON 

1.6 X 10^-19

f

FREQUENCY (1/time taken) therefore

1/f = time taken

E

ELECTRIC FIELD STRENGTH

E = F / Q (With test charges) 

E = V / d (For two parallel plates)

F

Force due to electric field strength

F = QE 

W

Work done

W = QEd 

W = QV(Volts)

ε_ο

Epsilon nought

8.85 x 10^-12 Fm^-1 (Farads per metre)

CONSTANT OF PROPORTIONALITY

COULOMB'S LAW

1 / 4πε_ο

9.0 x 10⁹mF^-1

                                                         K

COULOMB'S LAW

F = K x Q₁Q₂ / r²

Force = constant x charge 1 x charge 2 / distance sqaured

ELECTRIC FIELD STRENGTH

Inversely proportional to the square of distance r 

ELECTRIC POTENTIAL

Inversely proportional to distance r it's not an inverse square alw becasue v is proportional to 1/r.

V curve is always LESS steep than E curve

NEGATIVE E AND NEGATIVE V

Negative E = field acts towards negative charge

Negative V = value less than 0 

E varies with distance more sharply than V