AQA Physics A-level Section 7: Fields and Their Consequences Key Points
Gravitational fields A force field is a region in which a body experiences a non-contact force. Gravity is a universal force acting between all matter. The gravitational field strength is the force that a unit mass would feel at that particular point. Field lines point in the direction a mass would move; the denser the lines, the stronger the field. Uniform Field Radial Field
Gravitational potential Gravitational potential is the work done moving a unit mass from infinity to a point in the field. Gravitational potential is zero at infinity. V g is negative because you have to do work to move an object out of a field Combining these two formulas gives the more common formula (E=mgh) g is the gradient of a V g against r graph. The area under a g against r graph is V g Equipotentials are planes containing points with equal gravitational potential. This means that the amount of work done moving around these planes is zero.
Orbits A synchronous orbit has a time period of one day, and returns to the same place in the sky each day. A low orbit is between 160 km to 2000 km. A geostationary orbit has a time period of one day and stays over the same point on the earth's surface. It must be directly above the equator and travel in the same direction as the earth s rotation. Escape velocity is the velocity needed to escape a gravitational field.
Electric fields ε 0 = Permeability of free space = 8.85 x10-12 Fm -1 The electric field strength is the force experienced by a unit positive charge at a point in the field.
Electric potential Electric potential is the work done moving a unit charge from infinity to a point in the field. the area under a E against r graph is V V can be both positive or negative because of the different charges E is the gradient of a V against r graph.
Electric Fields Gravitational Fields The area under a graph of E against r is V The area under a graph of g against r is V The gradient of the graph of V against r is E The gradient of the graph of V against r is g
Capacitance The capacitance of a capacitor is the amount of charge it can store per unit of potential difference, measured in Farads. Capacitors store relatively small amounts of charge, but release it much more quickly than batteries Energy stored by a capacitor: Therefore the area under a Q-V graph is the energy stored, and the gradient is the capacitance.
Dielectrics When a polar dielectric is placed between the plates of a parallel plate capacitor, the molecules in it align in the electric field with the positive charges displaced towards the negative plate of the capacitor, called dielectric polarisation. The relative permittivity of a dielectric material is the ratio of its absolute permittivity to the permittivity of vacuum. Therefore the capacitance of a capacitor depends on the dielectric material used, the area of overlap of the plates, and the spacing between the plates.
Charging and discharging Charging: Discharging:
Time constant The time constant. Half life. t 1/2
Magnetic flux density
Forces on charged particles The external magnetic field interacts with the moving charged particle, causing a resultant force. This force acts perpendicular to its velocity and causes circular motion. The velocity increases but the frequency is kept constant because the distance traveled increases.
Electromagnetic induction Φ= Flux B=Flux density A= Area N = Number of turns If the rod cuts through magnetic field lines, the electrons inside will feel a resultant force and move towards one side creating an electric field and an emf.
Investigating flux linkage
Faraday s law and Lenz s law Faraday s Law: Induced e.m.f is directly proportional to the rate of change of flux linkage. Lenz s Law: The induced e.m.f is always in such a direction as to oppose the change that caused it. A magnet dropped through a coil will fall more slowly as a current is induced in the coil that causes a magnetic field which interacts with the magnet to slow it.
Generators As the coil rotates, the flux linkage varies sinusoidally between +BAN and -BAN. According to Faraday s law, the e.m.f is the rate of change of flux linkage. Increasing the speed/frequency of rotation or increasing the magnetic flux density will increase the maximum e.m.f. This creates an alternating current.
Alternating current An oscilloscope is used to show voltage against time. The time base controls how fast the wave moves across the screen (e.g 2ms per division) The Y-gain is the voltage per division (e.g. 2V per division.) V 0 is the peak voltage. However the average voltage is not the peak voltage, and therefore we find the root mean square. The rms is usually quoted when referring to a AC power supply.
Transformers An AC current flowing in the primary coil causes the iron core to magnetise and demagnetise continuously. Therefore the core must be soft magnet. This then induces a voltage in the secondary coil. If a transformer was 100% efficient the power in would equal the power out - however power is lost due to eddy currents. These are looping currents caused by the changing magnetic field which dissipate energy as heat. Eddy currents can be reduced by laminating the core. Heat is also dissipated as the wires heat up due to resistance. Electricity is transferred at low currents (high voltages) so wires don't get hot due to P= I 2 R Electricity is used in homes at low voltages for safety reasons.