Fields

• A force field is an area in which an object experiences a non-contact force.
• Force fields can be represented as vectors, which describe the direction of the force that would be exerted on the object, from this knowledge you can deduce the direction of the field.
• Force fields can also be represented as diagrams containing field lines, the distance between field lines represents the strength of the force exerted by the field in that region.
• Fields are formed during the interaction of masses, static charge or moving charges.
• Gravitational fields are formed during the interaction of masses.
• Electric fields are formed during the interaction of charges.
• Both fields follow an inverse-square law.
• In gravitational fields, the force exerted is always attractive, while in electric fields the force can be either repulsive or attractive.
• Both fields have equipotential surfaces.
• The Earth’s gravitational field is radial, however very close to the surface it is almost completely uniform.
• Gravitational field strength (g) is the force per unit mass exerted by a gravitational field on an object.
• Gravitational potential (V) at a point is the work done per unit mass when moving an object from infinity to that point.
• Gravitational potential at infinity is zero, and as an object moves from infinity to a point, energy is released as the gravitational potential energy is reduced, therefore gravitational potential is always negative.
• The gravitational potential difference ( ) is the energy needed to move a unit mass V Δ between two points and therefore can be used to find the work done when moving an object in a gravitational field.
• Magnetic flux ( ϕ ) is a value which describes the magnetic field or magnetic field lines passing through a given area, calculated by finding the product of magnetic flux density ( B ) and the given area ( A ) when the field is perpendicular to the area: A Φ = B.
• You can use the above equation to derive a general formula for the magnitude of emf induced by a straight conductor of length l, moving in a magnetic field of flux density B.
• The process of particles being accelerated and increasing their speed until they exit the cyclotron is repeated several times.
• When a conducting rod moves relative to a magnetic field, the electrons in the rod will experience a force, causing an emf to be induced in the rod, this is known as electromagnetic induction.
• Lenz’s law states that the direction of induced current is such as to oppose the motion causing it.
• When particles reach the edge of the electrode, they begin to move across the gap between the electrodes, where they are accelerated by the electric field, increasing the radius of their circular path as they move through the second electrode.
• Faraday’s law can be expressed in the following equation: ε = N Δ t ΔΦ, where ε is the magnitude of induced emf, and N is the rate of change of flux linkage.
• To demonstrate Lenz’s law, you can measure the speed of a magnet falling through a coil of wire, and its speed when falling from the same height without falling through the coil.
• Lenz’s law explains why a magnet takes longer to reach the ground when it moves through the coil.
• When particles reach the gap again, the alternating electric field changes direction, allowing the particles to be accelerated again.
• Magnetic flux linkage (N ϕ ) is the magnetic flux multiplied by the number of turns N of a coil: Φ AN N = B.
• Faraday’s law states that the magnitude of induced emf is equal to the rate of change of flux linkage.
• If charges have the same sign the force will be repulsive, and if the charges have different signs the force will be attractive.
• Like gravitational fields, electric fields can be uniform or radial and can also be represented by the following field lines: The field lines show the direction of the force acting on a positive charge.
• The magnitude of electrostatic forces between subatomic particles is magnitudes greater than the magnitude of gravitational forces, because the masses of subatomic particles are incredibly small whereas their charges are much larger.
• The orbital radius of a geostationary satellite can be calculated using the relationship T^2 = 4π2 GM × r^3, where T is the orbital period, GM is the gravitational parameter, r is the orbital radius, and M is the mass of the satellite.
• The electrostatic force between two protons is times greater than the gravitational force.
• Geostationary satellites are useful for sending TV and telephone signals because they are always above the same point on the Earth, eliminating the need to alter the plane of an aerial or transmitter.
• Low-orbit satellites require less powerful transmitters and can potentially orbit across the entire Earth’s surface, making them useful for monitoring the weather, making scientific observations about places which are unreachable and military applications.
• Many satellites must work together to allow constant coverage for a certain region.
• Electric field strength (E) is the force per unit charge experienced by an object in an electric field, which is constant in a uniform field, but varies in a radial field.
• There are three formulas to calculate electric field strength: E = Q F (for uniform fields formed by parallel plates), E = d V (for radial fields), E = 1 4πε 0 Q r 2.
• Coulomb’s law states that the magnitude of the force between two point charges in a vacuum is directly proportional to the product of their charges, and inversely proportional to the square of the distance between the charges.
• Low-orbit satellites have significantly lower orbits in comparison to geostationary satellites, therefore they travel much faster, meaning their orbital periods are much smaller.
• The equation for centripetal force and gravitational force can be equated: centripetal force C = r mv² and gravitational force G = r² GM m/r².
• Kepler’s third law states that the square of the orbital period (T) is directly proportional to the cube of the radius (r).