# Fields

AQA unit 4

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## Gravitational fields

Gravitational field- if an object is palced anywhere in a field tehn this object will feel a force this will be the pull of another objects gravity.

Field strength

The gravitational field strength at a point in a field is teh force per unit mass

F=mg

Newton's Law of gravitation

F=Gmm/r2

This is an example of an inverse squar law: F is proportional to 1/r2

The objects are point masses, as if all of an object's mass is concentarted at its centre of mass. Each of the two objects feels the same force but in oposite directions. They are an equal and opposite pair of forces, as described by Newton's third law.

g=Gm/r2

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## Gravitational Potential

Work needs to be done against the force of gravity to move a mass away from the Earth. This results in an increase in its gravitational potential energy.

For small movements ofa mass in the earths gravitational field

PE=mgh

Definfing gravitational potential

The gravitational potential (V), at a point in a gravitational field is the potential energy per unit mass at that point.

PE=mV

It can also be defined as the work done per unit mass in taking a small mass to infifnity from that point.

V=-GM/r

Potential and field strength

If a 1kg mass is moved a small distance r, its potential will change by V. The change in potential equals the work done on 1kg, which is the force on 1kg times teh distance moved:

-V=gxr

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## Geosynchronous orbits

A satellite in geosynchronous orbit will always remain above the same placeon the equator.This means that it can be used for relaying TV, telephone and other tellecommunications signals from one place on the Earth's surface to another. The satelitte must:

• Have a time period of 24 hours.
• Be in orbit above the equator.
• Move inthe same direction as the Earth is turning.
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## Polar orbiting satellites

Some satellites orbit the poles. Their time period depends on their height. They 'scan' the whole surface of the Earth as it rotates under teh orbiting satellite. Polar orbiting satellites are used for:

• Meteorology and weather forecasting.
• Military surveillance.
• Location of the Earth's resources.
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## Electric fields

Electric field strength

Any charged object placed in the field will feel a force. To define teh electric field strength at a point in the field:

E=F/Q electric field strength=force per unit charge

Charged parallel plates

There is a uniform electric field between a pair of parrallel plates. The plates can be charged by applying a voltage across them. The greater the voltage, the stronger the field:

E=V/d

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## Motion of a charged particle in a uniform electric

In a vacuum, an electron enters a uniform electric field between two parallel metal plates with a horizontal speed(parallel to the plates) of v. The p.d. across the field is V. The electron experiences a constant downward force, F, of magnitude QE towards the positively charged plate, where E=V/d. Since teh force is constant, the acceleration towards the plate is constant. The horizontal component of teh electrons speeddoes not change. There are no air molecules to slow the electron down.

Since there is a constant vertical acceleration and a constant horizontal speed, the path of the electron is a parabola.

To calculate the downward acceleration:

F=ma=QE=QV/d

therefore a=QV/md

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