Understanding Force Fields: Gravitational & Electric

Fields

• A force field is an area in which an object experiences a non-contact force.
• Force fields are represented as vectors, which describe the direction of the force.
• Diagrams containing field lines are also used to represent force fields.
• The distance between field lines indicates the strength of the force.
• Force fields form during the interaction of masses, static charges, or moving charges.
• Gravitational fields form during the interaction of masses.
• Electric fields form during the interaction of charges.

Similarities & Differences of Force Fields

• Forces in both gravitational and electric fields follow an inverse-square law
• Field lines represent both gravitational and electric fields
• Gravitational forces are always attractive.
• Electric forces can be either repulsive or attractive.
• Electric force acts on charge.
• Gravitational force acts on mass.
• Both have equipotential surfaces.

Gravitational Fields & Newton's Law

• Gravity acts on any object with mass and is always attractive.
• Newton’s law of gravitation states gravitational force between two masses is:
• Directly proportional to the product of the masses
• Inversely proportional to the square of the distance between them
• The formula: F = Gm₁m₂/r², where G is the gravitational constant, m₁/m₂ are masses, and r is the distance.

Gravitational Field Strength

• Two types of gravitational fields include uniform and radial fields
• Field lines' arrows indicate the direction of force on a mass
• A uniform field exerts the same gravitational force on a mass everywhere, represented by parallel, equally spaced field lines
• In a radial field, exerted force depends on the object's position. Force decreases as distance from the center increases
• Earth's gravitational field is radial but nearly uniform near the surface
• Gravitational field strength (g) is the force per unit mass exerted by a gravitational field
• g is constant in a uniform field and varies in a radial field
• Formulas to calculate g: g = F/m (general) and g = GM/r² (radial fields only)

Gravitational Potential

• Gravitational potential (V) at a point is the work done per unit mass against gravitational force to move an object from infinity to the point
• Gravitational potential at infinity is zero
• Energy releases as gravitational potential energy is reduced, so gravitational potential is always negative
• Formula for V in a radial field: V = -GM/r, with M as the object's mass causing field and r as the distance.
• Gravitational potential difference (ΔV) is the energy needed to move a unit mass between two points.
• Work done = mΔV, where m is the mass of the object moved.

Equipotential Surfaces

• Equipotential surfaces are created by joining points of equal potential
• Potential on an equipotential surface is constant everywhere
• No work is done when moving along an equipotential surface because gravitational potential difference is zero
• Equipotential surfaces are represented as red lines in the diagram example provided.
• Gravitational potential (V) is inversely proportional to the distance between the centers of two objects
• Represent V against distance r on a graph.

Gravitational Field Strength Measurement

• Gravitational field strength (g) at a distance is measured by drawing a tangent to the potential (V) graph
• Gradient is calculated before multiplying by -1
• Formula: g = -ΔV/Δr
• Gravitational potential difference can be found by calculating the area under a graph of gravitational field strength (g) against distance (r)

Orbits of Planets & Satellites

• Kepler's Third Law: T² ∝ r³, where T is the orbital period and r is the radius
  • An object orbiting a mass experiences gravitational force (centripetal force)
  • Equate centripetal force and gravitational force: mv²/r = GMm/r²
  • Rearrange equation to make v² the subject: v² = GM/r
  • Formula for v in terms of r and T: v = 2πr/T ⇒ v² = 4π²r²/T²
  • Substitute: 4π²r²/T² = GM/r
  • Rearrange to make T² the subject: T² = (4π²/GM) × r³
  • Since (4π²/GM) is constant: T² ∝ r³
• Total energy of orbiting satellite has kinetic & potential energy and remains constant
• If satellite height decreases:
  • Gravitational potential energy decreases
  • Kinetic energy increases (higher speed)
  • Total energy is constant

Escape Velocity

• Escape velocity: minimum velocity to escape gravitational field at a mass's surface
• Object's kinetic energy equals the magnitude of its gravitational potential energy
• mv² = GMm/r, and gravitational potential is mΔV
• v = √(2GM/r)
• Escape velocity doesn't depend on the object's mass

Synchronous Orbit

• Synchronous orbit: orbital period of satellite equals rotational period of object orbited
• Example: satellite orbiting Earth, period is 24 hours

Geostationary Satellites

• Geostationary satellites: geosynchronous orbit; period is 24 hours
• Satellites stay above the same point orbiting directly above the equator
• Useful for sending TV and telephone signals consistently

Orbital Radius

• To find orbital radius of geostationary satellite: T² = (4π²/GM) × r³ ⇒ r³ = (GMT²)/4π²
• r³ = 6.67×10⁻¹¹×5.97×10²⁴×(24×60×60)² / 4π² = 7.53 × 10²² m – r = 4.2 × 10⁷ m (around 36,000 km above Earth's surface)

Low-Orbit Satellites

• Low-orbit satellites: lower orbits; travel faster; smaller orbital periods Require less powerful transmitters
• Orbit across entire Earth’s surface
• Useful for:
  • Monitoring the weather
  • Scientific observations of unreachable places
  • Military applications
  • Communications (require constant collaboration to avoid transmission problems)

Electric Fields & Coulomb's Law

• Coulomb's law states magnitude of force between two-point charges in a vacuum:
  • Directly proportional to product of charges
  • Inversely proportional to square of distance
• Formula: F = (1 / 4πε₀) × (Q₁Q₂ / r²), where ε₀ is permittivity of free space, Q₁/Q₂ are charges, r is distance
• Air as a vacuum is viable when using formula
• Assume charge acts at the center of charged sphere

Forces

• Forces are repulsive if charges have the same sign.
• Forces are attractive if charges are different. Electrostatic forces between subatomic particles are far greater than gravitational forces, because masses of subatomic particles are smaller, and electrostatic forces are much larger.
• Example: gravitational force (F = 4.65 × 10⁻⁴¹ N), electrostatic force (F = 5.75 × 10⁻⁵ N) between two protons 2 × 10⁻¹² m apart.
• Electrostatic force between two protons is 1.24 × 10³⁶ times greater than gravitational force

Electric Field Strength Formula

• Electric field strength (E): force per unit charge on object in an electric field - Constant in uniform field - Varies in radial field
• Formulas:
  • E = F/Q (general)
  • E = V/d (uniform field formed by parallel plates)
  • E = 1 / (4πε₀) × (Q / r²) (radial fields) V is voltage; d is distance; Q magnitude of charge; r distance.
• Represented by field lines
  • Uniform electric fields = same electric force everywhere; shown with parallel, spaced lines.
  • In radial field electric magnitude of force will be dependant in distance between the two charges

Work Done

• Work done by moving charged particle between parallel plates of uniform field:
  • Work done: F x d
  • E=F/Q ; F = EQ
  • E = Δv/d ; d = Δv/E
• Work done = QΔV
• Uniform electric fields find charges of particles fired at right angles and observing particle path
  • Constant electric force accelerates particles, forming a parabolic shape.
  • Positive charges follow field direction.
  • Negative charges move opposite field.

Electric Potential

• Absolute electric potential (V) at a point is the potential energy per unit charge of positive point charge at that point in the field
• Absolute Potential: greatest at charge surface, & decreases as charge increases
• Electric Potential: zero at infinity
• Electric Potential with radial field formula
  • V = 1/(4pie0) * (Q/r)

Dependency

• Value of potential is negative/positive depends on the charge sign (Q)
• If charge positive: potential is positive and repulsive
• If charge negative, potential is negative and attractive
• gradient of a tangent to a potential (V) against distance (r) graph, gives the value of electric field strength (E):
• gradient to find electric strength
• E = (delta V) / (delta r)

Electric Potential Difference

• Electric Potential Difference (ΔV)= energy to move unit charge btwn two points
• W= QΔV
• Electric fields have equipotential surfaces (like gravitational)
• Potential on equipotential surface is the same throughout
• No work done by charge if it moves along an equipotential surface
• Between two plates the equipotential surfaces are planes where equipotential forms concentric circles
• Plot electric field strength against distance

Capacitance

• The charge stored as a result of a unit potential difference is known as capacitance
• C= Q/V
• Made of conducting plates with a gap that could be seperated by

1. Dielectric When capacitor is connected to power, opposite charges are built and creates uniform field

Dielectric

• Ability of a material to store electric field is called its Permittivity
• Finding out the Relative Permittivity , will also find Dielectric constant to calculate capacitance
• Calculate relative by calculating ratio space and permittivity of dielectric.
• Cr = c/c0
• Ae0er/d , shows the plate area
  • The distance relative permittivity and is formed of negative and positive ends shown in Dielectric

Capacitor increase

• With electric field it causes them all to move
• Negative turns as the positive gets rotated
• Each molecule own electric field makes opposiotion to strength decreasing capacitance
• Capacitance is increased via electric field strength through the field
  • Q = v or voltage
• Graph stores energy against potential to find straight line
• E=1/2 * Q* V
• Formula for capacitance (C), which has been tested through it and helps get more variations through these

1. V =1/2 C times 1/2 QV,
2. =Q2/2C

Capacitor Charge & Discharge

• To charge, connect to a circuit with power supply and resistor
• Data logger use to measure current against time, graph helps measure charge After current flows negative charges build on terminal
• Electrons repel initial plate move and equal opposite turn makes plates
• Potential differences increase and become greater
• Flow decreases due to what has occurred .Current decreases to almost zero
• To recharge resistor connect to closed resistor with resistor -logger has to measure it to graphs for each
• Discharging means current flow must occur in opposite direction.

Capacitor Time

• It must fall across exponentially and means has same taken of time and graphs and the time
• Potential charge graphs follow , and require function: 1)Charging

2. Discharging

• There is also a resistance, used for the following circuit and the time resistance of each circuit.
• There is resistance to capacitor, resistance must be used to value of time taken towards: 1)Discharge initial number, for values through current against voltage If we measure the charges we can work out the time through graphs and calculations.
• lnQ equation
• The time is taken for gradient on half or initial equation, helps solve other equation. T = 0.69

Examples

• Draw line and measure values based on points
• 600nf capacitor
• 5c charge calculation

Magnetic Fields

• Current passes the strength of the magnetic field through the unit.
• One tesla is 1N used to current perpendicular field
• A force happens when a wire goes in field Parallel goes to 0, as none needs to perpendicular find to current
• Fingure help find left.
• Fingers should be used correctly:
• Thumb (represents motion/force) -First (Indicates direction
  • Sencond (Opposite direction to electron)

Magnetic fields, North & South

moving charts & Magnetic Fields

• Force goes across particles with why a is through wire

  • contains which charged

• The magnitude can be calculated as following which help the velocity -f=BQV formula to what has happened with each calculation through what to do through direction with help of fingure

• Force needs perpendicular motion causes follow with chart

• F=BQv is equation

• m is the moss and Q is the charger

• Application helps with which can then many produces and trace to calculate

Cyclotron Forms

• Formed with semicircles electrodes and plane each help voltage in the electrodes

• Deflected in a circular part through not in the middle to follow each chart

• The force isn't directly linked so speed and charge should is linked to it

• In the end the alternating each field has to change on, there is needs repeated which gives a certain number 1)B

Magnetics

• Magnets each field line and direction , it is found by density per squared with perpendicular follows along the areas-
  • Magnetic flux = BA Which it followed and has sources that calculate

Magnetic flux linkage

• Magnetic times the run of coil
• N = BAN
• Flux and linkage can be known by resolving chart
• Parallel and to coil
• The chart makes 1 if chart is not to calculate

Induced formula

1. When coil has a rod which is moving it happens to all as electrons are force that side of the wire emf is induced and electromagnetics it forms a circuit

• Two Laws

Magnet Demo & Laws

• Faraday: induced if the rate is linked

• Linz: opposity causes

• The speed is messured down through coil that slows because slows a. Each magnetic slows down to make resistance

Electricity

• Electricity is the energy to create to what to does through circuit

• Electrical potential is the gradient which helps each value, which electrical field helps

  • E= a r value

Explore force fields focusing on gravitational and electric fields. Learn how fields are represented by vectors and field lines. Understand the similarities and differences between gravitational and electric fields, including the inverse-square law and attractive/repulsive forces.