Charges, voltage and current

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Lecture 2 1

Charges, voltage and current

Lecture 2 2

Atoms and electrons

• Atoms are built up from

– Positively charged nucleus

– Negatively charged electrons

orbiting in shells (or more

accurately clouds or orbitals)

+

-Negative charge = positive charge so atoms are

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Lecture 2 3

Electric charge

• Electric charge is measured in Coulombs

(symbol C)

Charles Augustin de Coulomb (1736 – 1806) Published the inverse square law of electrical attraction

The charge on the electron is - 1.6021892x 10-19_C

The charge on the proton is +1.6021892x 10-19_C

usually referred to as

e

This is a fundamental constant of our universe

The symbol that we use for charge in equations is

usually

Q or q

We can remove electrons from (some) atoms quite easily Heating

Electrical sparks Friction

Photo-electric effect

Separated electric charges have a very strong force between them (the electrostatic force)

Like charges repel Opposite charges attract

The force obeys the inverse square law

Free charges

+ +

- +

The positively charged atom left behind is called an ion

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Lecture 2 5

Inverse square law

1 2 2 0

4 q q

F

r

πε

=

ε

₀(epsilon nought) is called the permittivity of free space and is another fundamental constant of our universe which relates electrostatic effects to force (and so to energy)

ε₀= 8.854188x 10-12 _C2_N-1_m-2

Units: Newtons when charges are in

coulombs and distance in metres

+ + - + F F F F q₂ q₁ +q₂ -q₁ r Lecture 2 6

Inverse square law

1 2 2 0

4 q q

F

r

πε

=

The force between two charges of 1 C separated by 1 metre:

approximately 9,000,000,000 N or 916,000 tonnes!! 0 1 Newtons 4 F πε = + + - + F F F F q₂ q₁ +q₂ -q₁ r

The electrostatic force is by far the strongest physical force that we normally experience and is responsible for all of the

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Lecture 2 7

Electric field

The electrostatic force can be expressed in terms of ELECTRIC FIELD (symbol E)

A vector field surrounding charges with

magnitude proportional to the force on a point charge direction in the direction of the force on a positive charge

(i.e. electric field arrows point towards NEGATIVE charges)

F = qE

(units of E for now, N C-1₎

Electric field surrounding point

charges

+ -2 0

( )

4 q

E r

r

πε

=

E

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Lecture 2 9

Moving electrons

A free electron in an electrostatic field experiences a force and so it accelerates and gains kinetic energy.

The further it moves through the field, the more energy it gains.

E - F v=0 - F v d Lecture 2 10

Moving electrons

E - F v=0 - F v d

In a uniform field, force is constant, so velocity increases like

2 2 2 1 2 Eqd v m mv Eqd = =

The electron kinetic energy increases linearly with distance along the electric field

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Lecture 2 11

Direct application of fast electrons –

the cathode ray tube

Colour TV or monitor tube A. Electron gun

B. Glass vacuum envelope C. Beam deflection and focusing F. Phosphor screen

Small CRT e.g. for an oscilloscope

Carbon nanotubes for a modern Field-Emission Display

Potential differences – THE VOLT

+ + + + -K.E. P.E. 0 1 J 2 J 3 J 4 J 5 J 0 1 J 2 J 3 J 4 J 5 J + E Q=1 C P.D. 0 1 V 2 V 3 V 4 V

5 V _• _{A charge in an electric field has} POTENTIAL ENERGY

• As it moves through the field it gains KINETIC ENERGY

• The increase in K.E. for a charge of 1 C is called the POTENTIAL DIFFERENCE or ELECTROMOTIVE FORCE (e.m.f.)

This is such an important parameter that it has its own unit – the VOLT (derived from J C-1₎

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Lecture 2 13

THE VOLT (symbol V)

• A potential difference of

1 volt will give 1 joule

of kinetic energy to a

charge of 1 coulomb

Alessandro Volta (1745-1827) Credited with constructing the first chemical battery

Energy

=

QV

Lecture 2 14

A demonstration “Voltaic

pile” from ~1825

+ -+ -+

Two “dry piles”, insulated with sulphur

The metal ball suspended on a silk thread alternately charges + and – and oscillates between the bells Claimed to be the “world’s most durable battery” (Guinness Book of Records) or (popularly) a perpetual motion machine!

Clarendon Laboratory ‘Museum’, Oxford

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Lecture 2 15

An analogy

+ + + + -K.E. P.E. 0 1 J 2 J 3 J 4 J 5 J 0 1 J 2 J 3 J 4 J 5 J + E Q=1 C P.D. 0 1 V 2 V 3 V 4 V 5 V F=EQ P.E. = mgh K.E. = ½mv2

A charged particle moving in an electric field has exactly the same dynamics as a mass falling under gravity

who?

F=mg

A new definition for electric field

We can now define electric field in terms of VOLTAGE Remember that

Field is Force per unit charge (newtons per coulomb) Voltage is energy per unit charge (joules per coulomb) Energy is Force x Distance (joules = newton.metres)

so Voltage = Field x distance

Field = Voltage / distance: Units V m-1

+V

l E=V/l

In a uniform field, E=-V/l, V=-El

In a non-uniform field,

( )

l

dV

E l

dl

V

E l dl

= −

∫

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Lecture 2 17

Current

• Moving charged particles transport charge from one point to another

• The rate of charge transport across any surface is called the CURRENT [symbol in equations i or I, unit Ampères (A)]

If N particles of charge q cross a surface in time t, the current is given by Ampères Nq i t =

The early experimenters got it wrong. Current is carried by electrons and so we have to remember that current flow is OPPOSITE to electron flow.

Electrons: Negative to Positive Current: Positive to Negative

Lecture 2 18

André-Marie Ampère (1775-1836) Investigated the magnetic effects of electric currents

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Lecture 2 19

Current and charge

In practice, the flow of charge carrying particles is not constant with time so we have to use a differential definition for the instantaneous current at a particular time t:

( )

dq

i t

dt

=

where dq is the small amount of charge (C) which flows in the small time from t to t+dt (sec).

To get the total charge that has flowed in a particular time period we need to integrate the current:

2 1

( )

t t

Q

=

∫

i t dt

If current is constant, charge=current x time current = charge/time

Current flow and power

Moving electrons carry ENERGY as well as charge, and so an electric current has POWER (rate of arrival of energy)

[symbol in equations P, unit Watt = 1 Joule per second, W]

Similarly to current we can define the power as

( ) dE

P t dt

= where dE is the small amount of energy crossing our surface between t and t+dt

We already know that the energy of a particle of charge q coulombs with voltage V volts is qV joules, so

( )

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Lecture 2 21

James Watt (1736-1819)

Scottish engineer most famous for the development of steam power – he was the first to use the term ‘horse-power’

Lecture 2 22

Active and passive components

W +V I +V I W Passive:

• Current flow is in the direction of the voltage (+ to -)

• Power is absorbed from the current by the components and transferred to the surroundings

Active:

• Current flow is in the OPPOSITE direction to the voltage (- to +) • Power is absorbed from the

surrounding by the components and transferred to the current flow