Fields and Forces

Fields and Forces Topic 6

6.1 Gravitational Force and Field

"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 Gravitation 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.)

6.1.1 Law of Universal Gravitation 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.)

Universal gravitational constant = 6.67x10-11 m3kg-1s-2 in db 6.1.1 Law of Universal Gravitation 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.)

"The force per unit massexerted on a point." in db 6.1.2Gravitational Field Strength The definition of gravitational field strength can be garnered from the above equation that can be found in the databook.

6.1.2Gravitational Field Lines 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.

6.1.2Gravity near a Planet's Surface The 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.

6.1.2Gravity within a planet's surface Assuming 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.

Gravitational Field Strength (N/kg) Distance from centre of mass of planet (m) 6.1.2Gravity within a planet's surface Assuming 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.

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: 1.0N/kg to the left The total field at Q, which is the same distance as P from A: 4.3N/kg to the right 6.1.2Gravitational Field due to a combination of masses

6.2 Electrical Force and Field

6.2.1Types of Charge Electrical 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.

"For an isolated system, the total charge in remains constant." 6.2.2Conservation of charge When 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.

6.2.2Conservation of charge If 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." 6.2.3Conductors and Insulators If a charged particle comes into contact with a lesser charged particle, the charge will be transferred and distributed between the two particles.

6.2.3The 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.'

(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. 6.2.3Charging by induction

"The force between two point charges is proportional to the product of the charge and inversely proportional to the square of their separation." 6.2.4Coulombs Law 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.

in db is called the pemittivity of 'free space.' It is a measure of a vacuum to transfer an electric force and field. 6.2.4Coulombs Law 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.

For the arrangement of charges shown, calculate the resultant force on the central charge. Hint: a diagram will be helpful. 6.2.4Coulombs Law 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.

The mass of the spheres is 0.12g Calculate the charge on the spheres 6.2.4Coulombs Law 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.

"The force per unit chargeexerted on a small positive test charge." in db 6.2.5Electric field strength 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).

6.2.6Electric field strength Continuing with the theme of exchanging mass in the equation with charge, the following definition for electric field strength can be determined.

6.2.6Electric field due to one or more charges The diagrams show the 1D electric field acting on 3 test charges for similar charges (top) and opposite charges (bottom).

Determine the magnitude and direction of the electric field acting at the point. 6.2.6Electric field due to one or more charges The diagram shows a test charged placed inside the electric field between two charges of magnitude shown.

6.2.7Electric 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.

(For an electron) 6.2.7Electric 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.

6.2.7Electric 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.

6.3 Magnetic Force and Field

6.3.1Magnetic field due to a moving charge 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.

6.3.2Magnetic field due to currents 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.

6.3.2Magnetic 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."

6.3.2Magnetic 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.

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

6.3.3Force 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.

6.3.3Force 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.

in db 6.3.3Magnitude of the force on the current-carrying wire 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.

in db 6.3.4Magnitude of the force on a moving charge 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.

6.3.4Direction of the force on a moving charge 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.

6.3.4Mass spectrometers 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.

Fields and Forces