Fields and circular motion reivision

Newton's law of gravitation states that every object in the univere exeerts a attracts every other object in the universe with a force that is proportional to the product of the masses and universly proportional to the square of the distance between them.

F=-Gmm/rsquared

field strenth

This relates force to the mass of an object which feels a field. It is defined as the force [er unit mass at a point in the field. For the earth:

g=GMe/rsquared

Orbits

A satlitte is in stable orbit if the grvitational force on it exactly equals the centripal fore required for its orbit.

Gm/rsquared=vsquared/r

Coulombs law stats that the force between two point charges is directly proportional to the product of the charges, and inversally proportional to the square ofthe distance between them.

F=1/4pieE0 x q1q2/rsquared

Field strength

The field strength at a point in an electric field is the force acting per unit coulomb on charge placed at that point.

E=Q/4pieE0rsquared

V=-GM/r

Escape velocity- completely escape from the earths gravitational field.

The potential at a point in a gravitational field is equal to the work done in bringing unit mass from infinity to that point.

This is the work done in bringing a unit of +ve charge from infinity to a point.

V=Q/4pieE0r

V=1/4pieE0r x Q1Q2/rsquared

So p.d between two points is:

(Q/4pieE0r)-(Q/4pieE0r)

Force is negative because it acts in theopposite direction to displacement.

Work done in bringing a mass from infinity to the earths surface is given by the area under the graph.

Potential energy at a point = work doe in bringing a mass from infinity.

PE= -GMm/r

Size of force acting is given by:

F=BIl

This formula leads to a defintion of the tezla: If a conductor 1m long carrying a current of 1amp is placed at right angles to a magnetic field and has a force on it of 1N. Then the magnetic flux density is 1T. The direction of this force is gienby Fleming's LHR

A beam of particles is in effect, acting the same way as a current in a conductor.

F=BQV

The force direction can be found from Fleming's LHR [note that current direction is opposite to electron direction.]

Angular speed: omega=feta/t

Angular speed is measured in radians per second.

Linear speed v=r x omega

An object in in circualr motion is accelerating its direction is always changing. A force is required to do this. This is the centripetal force, and acts towards the centre of the circle.

F=mvsquared/r

F=mromegasquared.

F is the centripetal force

1. A radial field is where the field lines are like the spokes of a wheel, always directed to the centre. The force of gravity on a small mass near a much larger spherical mass is always directed to the centre of the larger mass.

2. A uniform field is where the gravitational field strength is teh same un magnitude and directionthroughout the field. The field lines are therefore parrallel to one another and equally spaced.

This is the process by which electricity is produed in something placed in a changing magnetic field.

There are two laws:

1. Faradays law- this states that the induced EMF is proportional to the rate of change of magnetic flux linked withthe circuit.

EMF isproportioal to fie/t

fie=BA

This is therefore to do with the size of the EMF.

2. Lenz's law- is to do with the direction of EMF. The law states that the emf is such to oppose the change producing it. Combiningthe laws.

EMF=-Nxfie/t