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AP Physics Review – coulomb’s law and electric fields Definitions Electrostatic Force –There is a mutual force two charges which is proportional to the product of the charges and inversely proportional to the distance between their centers of mass squared. qq F k 1 2 2 where k = 8.99x 109 Nm2/C2 r This force can be either attractive or repulsive depending on the signs of the charges. It is best to assign +/- according to the direction on an individual charge (b/c the force is a vector) rather than according to the signs. Therefore, when using the above equation I suggest plugging in all values as positive values and assigning the sign later. Electric Field, E - specifies the ratio of the force on a test charge to the magnitude of the charge FE Q itself. E k 2 where Q is the “source” of the field. qtest r o You can find the electric field due to a continuous distribution of charge via: dq E dE k r Where: for a linear distribution dq = λds. for a distribution across an area dq = σdA. for a distribution throughout a volume dq = ρdV. Electric field Lines – a visual representation of the electric field surrounding an isolated charge or a collection of charges. Four basic rules: o Field lines are drawn away from positive charges and toward negative charges. Lines are always perpendicular to the surface. o The number of field lines represent the relative magnitude of the field. o The density of the field lines indicates the magnitude of the field. o Field lines can NEVER cross! Electric Dipole – an arrangement of two charges that are equal in magnitude but opposite of sign that are separated by a given distance, d. o The axis that passes through the particles is known as the dipole axis o The electric dipole moment, p , is defined as p qd and is directed from the negative charge toward the positive charge. o When placed in an external electric field the electric dipole will experience a toque p E . The torque is maximum when the dipole moment is perpendicular to the electric field. The torque tends to rotate the dipole into the direction of the electric field (according to Coulomb’s Law), thus reducing the angle between p and E. o As the torque rotates the dipole, work is done according to W = τ θ. The work done by the field reduces the potential energy of the system –U = W. The dipole has its minimum energy when it is the equilibrium orientation (θ = 0) and its maximum energy when it is antiparallel (θ=180°). AP Physics Review – flux and gauss’s law Definitions Electrostatic Force –There is a mutual force two charges which is proportional to the product of the charges and inversely proportional to the distance between their centers of mass squared. qq F k 1 2 2 where k = 8.99x 109 Nm2/C2 r For Symmetrical distributions Gauss’s Law may be more convenient than Coulomb’s Law A Gaussian Surface* is a hypothetical closed surface that encloses a given amount/distribution of charge. The surface may be chosen as any shape; however, it is best to stick to the symmetry of the problem. Flux – describes the “number” of electric field lines that penetrate a given area. The area can be real (a physical surface) or imaginary (a Gaussian surface). Mathematically: E E dA or for a uniform electric field across a given area Φ=EA. Gauss’s Law relates the electric field on a closed surface* to the net electric charge enclosed by that surface. o E dA qencl o Pay attention to the sign! If Qencl is positive, the net flux is outward. Charges outside of the Gaussian surface ARE NOT included in Qencl. No matter how large the charge or how close it is to the surface. KNOW HOW TO USE THIS!!!!! Review your derivations – especially for spherical charge distributions and linear charge distributions. Charged Conductors o If excess charge is placed on an isolated conductor conductor, the charge will move to the surface of the conductor (due to the fact that like charges will repel). E=0 o The electric field inside a conductor is zero! If this were not true then there would always cavity be a force on charges within the conductor – the charges would experience a current. o If there is a void within a conductor there will be no net charge on the cavity walls. o To move a charge across the conductor requires NO work, therefore the potential (V) within the conductor is constant. This is b/c V = W/q and V = -Ed, so if E = 0, and W = 0. Shells o a shell of uniform charge attracts or repels a charged particle (that is outside of the shell) as if all of the shell’s charge were located at the center of the shell. o A shell of uniform charge exerts NO net force on a charged particle within the shell. AP Physics Review – Potential and Energy Electric Potential Energy (U) – the energy of an object due to the gravitational force. xr dU Fx and U (r ) U ( x) Fx dx dx x q1 q 2 UE k for energy set to zero at infinite separation R Voltage = Electric Potential (V) – the ratio of the work per unit charge. U kQ W V when Uo = 0 b/c R = ∞ q R q V = - E ds for a uniform field V = Ed Use the sign of the charge(s) in the above equations! These are scalar quantities so they do NOT have a direction associated with them! When in doubt about the signs – try to think about what is doing the work! Wfield = -Wapplied = -ΔU o If the field is naturally doing the work to move a charge, then the work done by the field is positive, the work done by an outside agent is negative and the change in potential energy is negative. o If an outside force is required to force a charge to move in a given direction then the work done by the field is negative, the work done by the outside force is positive and the change in potential energy is positive. Electronvolt (eV) – a unit of ENERGY that is equal to the work required to move an electron (or other particle with the elementary charge) through a potential difference of one volt. 1 eV = 1.6 x 10-19 J Equipotential surfaces – those upon which the potential is constant. If a given charge is moved across such a surface then its potential energy will remain constant. A charge can also be moved from such a surface back to the same surface without a change in total energy. Conductors Excess charge placed on a conductor will distribute itself across the outside surface. The net electric field w/I the conductor is zero AND the voltage across a conductor is constant! SO whatever the potential is at the surface of the conductor = the voltage within the conductor itself. It is important that you understand how capacitors are charged. This will help you to understand there function and how they affect a circuit. Capacitors – used to store energy, which is deposited slowly during charging, to be used in a quick burst at a later time. Therefore, it has a greater power output than the battery used to charge it b/c of the short release time (P= W/t). Q Capacitance – the ratio of the charge stored to the potential difference. C . The capacitance of a device depends V on its physical characteristics. They come in many shapes and sizes, but the most common is a cylindrical capacitor o A C . To determine the capacitance of another geometry first determine the potential: V E dR , then use d Q this to find the capacitance C . V Energy – remember that the function of a capacitor is to store electrical energy for use (independent from a voltage source like a battery) later. Therefore it is convenient to express the energy stored in the device. Recall that Q 1 Q2 W dW C qdq . Therefore, we can express the potential energy of a charged capacitor as: 0 2C Q2 1 U CV 2 2C 2 Capacitors in Circuits We can create circuits with capacitors in series and in parallel in a similar manner as we did for resistors. HOWEVER, due to the difference in the function of each device the rules are different. o Capacitors in series – all of the capcitors in series have the same charge (due to the charging process) so Q1 = Q2 = Q3 = …..The sum of the voltages in each capacitor in series is equal to the total potential supplied to the 1 1 1 collection. To find the equivalent capacitance of a collection of series capacitors apply: ... C C1 C 2 o Capacitors in parallel – all of the capacitors in parallel “see” the same potential, therefore V1 = V2 = V3 = …. The sum of the charge across each device is equal to the total charge supplied to the collection. To find the equivalent capacitance of the collection simply sum the individual capacitor values. Dielectrics – are insulating materials placed within the plates of a capacitor in an attempt to increase the capacitance by decreasing the electric field. A dielectric will increase the capacitance of a device by a factor of κ = the dielectric constant. This value is material specific and has no units.