Fields and Forces

Topic 6

GRAVITATIONAL FORCE AND FIELD6.1

6.1.1 Law of Universal GravitationNewton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. (Separately it was shown that large spherically symmetrical masses attract and are attracted as if all their mass were concentrated at their centers.)

"The force between two point masses is proportional to the product of the masses and inversely proportional to the square of their separation."

6.1.1 Law of Universal GravitationNewton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. (Separately it was shown that large spherically symmetrical masses attract and are attracted as if all their mass were concentrated at their centers.)

6.1.1 Law of Universal Gravitation

indb

Universal gravitational constant = 6.67x10-11 m3kg-1s-

2

Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. (Separately it was shown that large spherically symmetrical masses attract and are attracted as if all their mass were concentrated at their centers.)

6.1.2 Gravitational Field StrengthThe definition of gravitational field strength can be garnered from the above equation that can be found in the databook.

"The force per unit mass exerted on a point."

indb

6.1.2 Gravitational FieldLines of gravitational force can be drawn for all objects with mass. This leads to the following diagrams for spherical objects. Gravity is always attractive and points towards the centre of mass of the object. For a small area of the Earth, the ground can be considered flat, and all lines of force assumed to be vertical.

6.1.2 Gravity near a Planet's SurfaceThe acceleration due to gravity (gravitational field strength, g) depends on the distance from the centre of the planet and the mass of the planet. This equation can therefore be applied to other planets whereby their masses can be estimated.

6.1.2 Gravity within a planet's surfaceAssuming that all the mass of the planet is concentrated at its centre the gravitational field strength can be estimated for within the planet as well as at its surface. This can be done by substituting the equation for the mass of a spherical volume into the equation for gravitational field strength.

6.1.2 Gravity within a planet's surfaceAssuming that all the mass of the planet is NOT concentrated at its centre the gravitational field strength increases linearly according to the second equation and then decreases inverse-squarely once the planets surface is reached according to the first equation.

Gra

vita

tiona

l Fie

ld S

tren

gth

(N/k

g)

Distance from centre of mass of planet (m)

6.1.2 Gravitational Field due to a combination of masses

Point P is midway between A and B. At P the gravitational field strength due to A is 4.0N/kg and that due to B is 3.0N/kg

Taking right to be positive, the total gravitational field at P is:

The total field at Q, which is the same distance as P from A:

1.0N/kg to the left

4.3N/kg to the right

ELECTRICAL FORCE AND FIELD6.2

6.2.1 Types of ChargeElectrical charge comes in two types - positive and negative. On a small level, the amount of charge is quantized and comes in "packets" of 1.6x10-19C. Where C is the unit Coulomb. Like charges repel each other, like similar poles on a magnet. Unlike charges attract.

6.2.2 Conservation of chargeWhen charged particles combine, the overall charge is simply the sum of the individual charges. The sign on the charge must be taken into account also.

"For an isolated system, the total charge in remains constant."

6.2.2 Conservation of chargeIf a charged particle comes into contact with a lesser charged particle, the charge will be transferred and distributed between the two particles.

6.2.3 Conductors and InsulatorsIf a charged particle comes into contact with a lesser charged particle, the charge will be transferred and distributed between the two particles.

"An electrical conductor is a material through which charges can flow. An insulator is a material through which charges cannot flow."

"A metal is an example of a good conductor. It has many 'free electrons' (delocalized electrons)"

"When a conductor is heated, the increased vibrations of the atoms get in the way of the electrons thus increasing the resistance. With insulators, the heat actually causes the electrons to be freer, making it a better conductor."

The rubbing of a cloth onto a object can transfer electrons between them. The direction of transfer depends on the materials that both the cloth and object. The direction is determined by their position in the 'Triboelectric series.'

6.2.3 The Triboelectric effect

The rubbing of a cloth onto a object can transfer electrons between them. The direction of transfer depends on the materials that both the cloth and object. The direction is determined by their position in the 'Triboelectric series.'

6.2.3 The Triboelectric effect

6.2.3 Charging by induction

(a) Two metal conductors of initially no charge, are placed in contact.

(b) A charged rod is brought close to one of the spheres. This attracts the unlike charge towards it and repels the like charge away from it.

(c) Separate the metal spheres. The repelled charge is "removed" on the metal sphere.

(d) Now that each metal sphere holds opposite charges, they will experience an attractive force.

The law was first published by Charles Augustin Coulomb in 1783. Its similarity with the gravitation law shows just how similar the field theories are.

6.2.4 Coulombs Law

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

The law was first published by Charles Augustin Coulomb in 1783. Its similarity with the gravitation law shows just how similar the field theories are.

6.2.4 Coulombs Law

indb

is called the pemittivity of 'free space.' It is a measure of a vacuum to transfer an electric force and field.

The law was first published by Charles Augustin Coulomb in 1783. Its similarity with the gravitation law shows just how similar the field theories are.

6.2.4 Coulombs Law

For the arrangement of charges shown, calculate the resultant force on the central charge. Hint: a diagram will be helpful.

The law was first published by Charles Augustin Coulomb in 1783. Its similarity with the gravitation law shows just how similar the field theories are.

6.2.4 Coulombs Law

The mass of the spheres is 0.12g

Calculate the charge on the spheres

Continuing with the theme of exchanging mass in the equation with charge, the following definition for electric field strength can be determined.The term test charge is used here, because a normal charged particle would have its own electric field that would interfere with this electric field due to the object. The unit of electric field strength is Newton per Coulomb (N/C).

6.2.5 Electric field strength

indb

"The force per unit charge exerted on a small positive test charge."

Continuing with the theme of exchanging mass in the equation with charge, the following definition for electric field strength can be determined.

6.2.6 Electric field strength

The diagrams show the 1D electric field acting on 3 test charges for similar charges (top) and opposite charges (bottom).

6.2.6 Electric field due to one or more charges

The diagram shows a test charged placed inside the electric field between two charges of magnitude shown.

6.2.6 Electric field due to one or more charges

Determine the magnitude and direction of the electric field acting at the point.

It is common for multiple choice question to test on the electric field patterns for single or arrangements of electric charges. The field always emanates from positive charges, and points towards negative charges.

6.2.7 Electric field patterns

It is common for multiple choice question to test on the electric field patterns for single or arrangements of electric charges. The field always emanates from positive charges, and points towards negative charges.

6.2.7 Electric field patterns

(For an electron)

Recall from topic 5 that the work done in moving a charge from one plate to another. If we equate this to the traditional Force x Distance equation we can determine another (important!) equation for electric field strength. Note here that the units is V/m rather than the equivalent N/C.

6.2.7 Electric field due to parallel plates

Recall from topic 5 that the work done in moving a charge from one plate to another. If we equate this to the traditional Force x Distance equation we can determine another (important!) equation for electric field strength. Note here that the units is V/m rather than the equivalent N/C.

6.2.7 Electric field due to parallel plates

MAGNETIC FORCE AND FIELD6.3

A moving charge (positive or negative) causes a magnetic field of its own. The magnetic field pattern is that of a circular field, concentric, getting weaker as you get further away. This translates to a very similar pattern of a magnetic field around a current-carrying wire.

6.3.1 Magnetic field due to a moving charge

It is important that the field patterns for a variety of current carrying wires is known. Here shown is the magnetic field around a single straight wire. The direction of the magnetic field is given by the Right-Hand-Screw-Rule as shown. The RHSR is VERY important.

6.3.2 Magnetic field due to currents

Here is shown the magnetic field around a single loop of wire. The direction of the field can be determined by using the screw-rule twice. Once on each side of the loop (as it goes in and out of the "paper."

6.3.2 Magnetic field due to currents

Shown here is the magnetic field of a solenoid. The direction of the current in the wire is shown by the dot and cross. The screw-rule can be used here to determine the direction of the magnetic field. The overall pattern is very similar to that of a bar magnet.

6.3.2 Magnetic field due to currents

To determine the FORCE on a charge or wire inside a magnetic field we use FLEMINGS LEFT HAND RULE. Use this in cases of force on a wire.

6.3.3 Force on a current-carrying wire in a magnetic field

We have already seen that a force is felt by a current carrying wire inside a magnetic field. The current carrying wire produces its own magnetic field which interacts with the magnetic field of the magnet.

6.3.3 Force on a current-carrying wire in a magnetic field

The current here is into the page and the magnetic field from the permanent magnets is from the bottom to the top. The magnetic field due wire is clockwise. (Screw-rule). In the shaded box all the magnetic fields are pointing the same way. The allows the fields to be more dense on one side compared to the other. This imbalance exerts a force to the right and is sometimes called a "catapult field." This can be checked using Fleming's Left.

6.3.3 Force on a current-carrying wire in a magnetic field

The force exerted on the wire is the product of the current, length of wire inside the magnetic field and the perpendicular component of the magnetic field vector. This introduces an angle between the field and the wire. This is known as the Laplace Force Equation.

6.3.3 Magnitude of the force on the current-carrying wire

indb

As previously discussed, a moving charge generates its own magnetic field that can interact with a permanent magnetic field. Just like the electrons in a wire, a single charge can also experience a force. However, instead of using the length of the wire, we use the distance travelled in a unit time and instead of using current we need to use the magnitude of the charge itself.

6.3.4 Magnitude of the force on a moving charge

indb

A charged particle moving in a magnetic field with experience a force which is always directed towards the centre of a circle. This causes it to experience uniform circular motion, which it is constant accelerated in the direction of the force. By equating the magnetic force with the centripetal force we can determine the mass of the charged particle.

6.3.4 Direction of the force on a moving charge

Charged particles are accelerated through a PD and enter a region of uniform magnetic field. This causes it to travel in a circular path in a radius proportional to its mass. If a screen or sensor is positioned just so, the mass and thus the identity of the particle can be identified.

6.3.4 Mass spectrometers