Topic 6: Fields and forces State Newton’s universal law of gravitation. Students should be aware that the masses in the force law are point masses. The force between two spherical masses whose separation is large compared to their radii is the same as if the two spheres were point masses with their masses concentrated at the centers of the spheres. 6.1 Gravitational force and field

Newton Newton’s laws of gravitation Anything with mass attracts anything else with mass. The size of that attraction is given by my Law of Gravitation: F = Gm 1 m 2 r 2 …where m 1 and m 2 are the masses of the two objects (in kg), r is the distance between them (in m) and G is “The Universal Gravitational Constant” (= 6.67 x Nm 2 kg -2 ). State Newton’s universal law of gravitation.

Cavendish measurement of G Click to play

Inverse square law

What holds the planet in orbit?

Free Body Force Diagrams revision The Earth attracts the man and the man attracts the Earth – a Newton III pair of forces where both are gravitational.

A uniform gravitational field is one where the field lines are always the same distance apart - this is almost exactly true close to the Earth's surface (Figure 1(a)). However if we move back and look at the planet from a distance the field lines clearly radiate outwards (Figure 1(b)), getting further apart as the distance from the Earth increases. When viewed from an even greater distance the complete field can be seen (Figure 1(c)). Such a field is called a radial field - the field intensity (g) decreasing with distance. Diagram 1(d) shows the distortion of the gravitational field lines by high- density rock.

Gravitational Field Strength Consider a man on the Earth: Man’s weight = mg BUT we know that this is equal to his gravitational attraction, so… GMm = mg r 2 GM = g r 2 Therefore: (this is a vector quantity) Derive an expression for gravitational field strength at the surface of a planet, assuming that all its mass is concentrated at its centre.

Gravitational Field Strength Define gravitational field strength. Definition: Force, act, point, unit mass. Write a definition of gravitational field strength Determine the gravitational field due to one or more point masses. Derive an expression for gravitational field strength at the surface of a planet, assuming that all its mass is concentrated at its centre.

6.2 Electric force and field State that there are two types of electric charge.

Static Electricity

Conservation of charge The law of conservation of charge states……………. One of the fundamental laws of Physics is that charge can never be created or destroyed. Charge is always conserved in any reaction. A simple example of this is the rubbing of a polythene strip with a duster. Initially the strip and the dusted were uncharged but after rubbing the strip gains a net negative charge and the duster gains an equal amount of positive charge – the total charge in the process has been conserved. State and apply the law of conservation of charge.

Conductors and insulators. Describe and explain the difference in the electrical properties of conductors and insulators. In a conductor, the conduction and valence bands overlap. This allows the valence electrons to easily move along the conduction band giving the material low electrical resistance. In insulators, there is a large forbidden energy band, which makes it difficult for valence electrons to move into the conduction band giving the material a high electrical resistance. In semiconductors, the forbidden energy band is not too wide. Under certain conditions, electrons in the valence band can gain sufficient energy to cross the gap. This reduces the electrical resistance of the material. The difference between conductors and insulators is………………

Coulomb’s law State Coulomb’s law. Students should be aware that the charges in the force law are point charges.

Coulomb’s Law Charles Coulomb Like gravity, electrostatic force is one of the four fundamental forces. The equation looks pretty similar too… Coulomb’s Law F = kQ 1 Q 2 r 2 …where k = 9.0 x 10 9 Nm 2 C -2 (the “Coulomb Law Constant”). This comes from k = 1/4 πε 0 … …where ε 0 = permittivity of free space (i.e x Fm -1 ).

Electric field of a point charge Define electric field strength. Write a definition of electric field strength Students should understand the concept of a test charge. Determine the electric field strength due to one or more point charges.

Electric field patterns Draw the electric field patterns for different charge configurations. These include the fields due to the following charge configurations: a point charge, a charged sphere, two point charges, and oppositely charged parallel plates. The latter includes the edge effect. Students should understand what is meant by radial field.

How do we predict the shape of a field? Imagine that you have a unit positive test charge. Place it in a point in the field. Sketch the path it would take. Repeat this many times until you have enough field lines The “density” of the lines represents the strength of the field.

Point charge +

Sphere Positive or negative

2 Point charges ++

+ -

Parallel plates + _ Edge effects

Electric Fields Electric field strength E = F q (this is a bit like gravitional field strength g = F/m) Let’s compare this to Coulomb’s Law: Coulomb’s Law F = kQq r 2 Putting these equations together gives us… Electric field strength E = kQ (in NC -1 ) r 2

Electrostatic force and circular motion Consider an electron orbiting a nucleus in a hydrogen atom: p e Q. If the mass of an electron is 9.1x kg and the distance to the proton is 0.11nm how fast is the electron going? Using mv 2 = kQq we get v = 1.5x10 6 ms -1 rr 2

A practical example Consider a charged polythene strip and a metal ball:

Fields applet

Field for a point charge Click to play

Electric dipole Click to play

Falstad.com

Electric fields around a point charge Draw the edge effects for the parallel plate 2 Charged Spheres

Uniform electric fields Consider two charged plates: + - Now consider a point charge: Q V Work done = QV For an electron, eV = ½mv 2

Visualising the fields Hyperlink

6.3 Magnetic force and field

Permanent magnets and domains

Hyperlink State that moving charges give rise to magnetic fields. Draw magnetic field patterns due to currents. These include the fields due to currents in a straight wire, a flat circular coil and a solenoid.

Field around a wire Click to play

Field around a loop Click to play

B field for a loop Click to play

Field patterns

Left hand Motor Rule Determine the direction of the force on a current-carrying conductor in a magnetic field.

Fleming's left- hand rule

Current-carrying wire in a magnetic field S N F = Force B = Magnetic field I = Current Q. Where will this wire go?

Comparing magnets and solenoids N S Magnet: Solenoid:

Magnetic Field around a Solenoid

Forces on a loop Click to play

Electric motor Click to play

Hyperlink

Magnetic Flux Density Clearly, the size of the force on this wire depends on three things: 1.The strength of the magnetic field 2.The current in the wire 3.The length of the wire (in the field) These three things are related by the simple formula… B is called “magnetic flux density” and is measured in Teslas (= 1NA -1 m -1 ). By definition, a magnetic flux density of 1T produces a force of 1N on a 1m long wire with a current of 1A.

Determine the direction of the force on a charge moving in a magnetic field. Hamper HL page 208 Q’s 37,38 SL Page 141 Q’s 8,9.

Force on a charged particle

Define the magnitude and direction of a magnetic field. A magnetic flux density of 1T produces a force of 1N on a 1m long wire with a current of 1A.

         Circular paths Recall: protons, 2 neutrons, therefore charge = +2 1 electron, therefore charge = -1 Because of this charge, they will be deflected by magnetic fields: These paths are circular, so Bqv = mv 2 /r, or r =mv Bq

Circular paths if angle = 90° the path is circular if 0 < angle < 90° the path is a helix. How do you work out which bit is circular?