PHYSICS II - Supplemental Guide
- 1. Supplemental study guide PHYS II 4 basic ideas to remember when dealing with Electricity and Magnetism. 1. All charges (moving or stationary doesn’t matter) create Electric Fields*. 2. All moving charges create Magnetic Fields**. (spinning counts too!) *Electric field lines always point away from Positive and towards Negative charge. **Magnetic field lines always point away from North and towards South pole
- 2. Supplemental study guide PHYS II 3. Electric Fields exert Force on charges.(moving or stationary doesn’t matter!) 4. Magnetic Fields exert Force on moving charges. (again spinning counts as well!)
- 3. Supplemental study guide PHYS II The intention of this supplement guide is to hit topics which are important but sometimes difficult to really have a good grasp or a good picture of. All in all the purpose is to make the student more comfortable with the topics. This supplement guide would try to help visualize and understand concepts using self-explanatory images. In simple words, this document could play the role of a secondary booster to help students to catch up with topics in Electricity and Magnetism. Coulomb`s Law: Like any two objects with ‘mass’ experience a Gravitational force between them, any two objects with ‘charge’ on them would experience an Electric force between them. Coulomb`s Law gives the formula to calculate this force.
- 4. Supplemental study guide PHYS II What is Voltage ? From the analogy below, voltage can be thought of, as a quantity that is just like (g*h) in Gravitation Fields. Assuming a uniform electric field throughout space (like in case of charged infinite parallel plates), both a stronger field or greater distance between two points in space makes the Voltage across those two points stronger.. and so can do more work. Like we have Gravitation P.E. we also have Electric P.E. defined at every point in space. Voltage is thus the Electric P.E. per (of a) unit charge
- 5. Supplemental study guide PHYS II What is a Capacitor ? Any two conducting surfaces (usually flat plates) separated by a distance can make a Capacitor. Capacitors have opposite charges on these two surfaces, which are very close to each other but the charges cannot make the jump across the surface, as the resistance in between is kept very high. Hence these charges get accumulated at the surfaces out of temptation, attracted towards the opposite charges, but are stranded there. Capacitors are hence devices that can store charge. We only have to apply a Voltage across the surfaces and an electric current would flow for a fraction of time, till the charges get accumulated to their full capacity on the surface. Capacitance C gives the measure of how much charge Q the capacitor can store, given a voltage V across the plates. Hence C is Q per unit V.
- 6. Supplemental study guide PHYS II What is current? Electric Current is rate of flow of electric charge with respect to time. Therefore , I = Δq / Δt Whats DC and AC ? DC (Direct Current): we apply a steady voltage Vo to the circuit and as a result there is a steady current Io flowing in one direction. AC(Alternate Current): we apply a periodically changing voltage V = Vo sin ωt and as a result observe a current I = Io sin ωt which changes directions all the time. If you observe the graph the direction of current changes every time it crosses the zero horizontal line. Magnetic Field due to current carrying wire. In general, Electric Current flowing through any wire produces a magnetic field around it (Biot-Savart Law). And since Magnetic Fields exert Forces on moving charges, it can in turn interact with other current carrying wires in vicinity.
- 7. Supplemental study guide PHYS II Force on moving positive charge and on a straight current carrying wire due a uniform Magnetic Field. Note that the Force F is a cross product of qv with B for the charged particle and Il with B for the current carrying wire. So, the direction of the force can always be determined by following the right hand cork rule. Also, both the formulae actually have the same physics involved. In other words at a differential scale we can roughly say qv = q(l/t) = (q/t)l = Il.
- 8. Supplemental study guide PHYS II Torque on current carrying Loop due to a uniform Magnetic Field. A current loop in a uniform magnetic field experiences a force couple, separated by distance b as shown above. The torque due this force couple, separated by distance b, is given as shown above. This formula is valid for any shape of a flat loop. The quantity NIA is called the magnetic dipole moment (M) of the coil.
- 9. Supplemental study guide PHYS II What are Magnets? In materials like Iron, Nickel and Cobalt there are unpaired electrons spinning around the nucleus which create a small magnetic dipole. If majority of such charges create magnetic dipole in the same direction the whole block has a considerable amount of net magnetic dipole and we would call it a magnet. Observing the nature of birth of magnetism, we know that a magnetic monopole cannot exist, since whenever a magnetic field is formed due to spinning charges a north and a south pole (dipole) is formed at the very same time.
- 10. Supplemental study guide PHYS II How to make an Electromagnet? Charges going in a loop generate strong Magnetic Field inside the loop We can make charges go in a loop by making loops of conducting wire and running a constant current through it. The direction of the conventional current that we indicate is the direction of the assumed positive charges. (Negative charge running left is same as saying positive charge running right). Hence constant current running through coils can generate a constant Magnetic dipole. These coils are called solenoids and the concentrated Magnetic Field inside the coil can be given by the following. FARADAY`s discovery .. ELECTROMAGNETIC INDUCTION Electromagnetic induction is a fancy way of referring to Faraday`s revolutionary discovery, which was the simple yet mystical phenomenon that Electricity and Magnetism talk to each other. In other words, changing one affects the other. For example a change in Magnetic flux across the area of a loop of wire creates and electric current in the wire. So, if say, you had a closed circuit with a bulb on it you could light that bulb just by moving a magnet through the area of the loop of the wire rapidly enough. Amazing isn’t it. In fancier words a changing Magnetic flux induces an emf. This emf (electromotive force which is like a voltage and not a force really) induces a current in a loop of wire called induced current. Lets check the physics now, in our light bulb example, what is changing really is the Magnetic flux through the loop. As a result en emf is induced such that, it would oppose that change in Magnetic flux..
- 11. Supplemental study guide PHYS II What is Flux ? Flux is the measure of amount of something passing perpendicular through some known Area. So, Electric flux is the measure of Electric Field lined passing perpendicular through some Area. Also similarly, Magnetic flux would be the measure of Magnetic field lines passing through some known Area of concern. The formulae are as below. The rate of change of this Magnetic Flux determines how much (opposing) emf would be produces in the loop(s) of wire. The formula can be given as follows This induced emf will make a current flow though the loop(s) such that the magnetic field produced by that current carrying loop will be opposing the original change in magnetic flux.
- 12. Supplemental study guide PHYS II In the cartoon below we have a coil and some constant Magnetic flux already passing through the coil. The constant magnetic flux is only assumed due the fact that we cannot make it zero so easily since earth has its own magnetic field which is always there. The cartoon also shows, a very rough after math of Faradays Induction Law. What is an Inductor ? (something that resists change in current) Inductance gives you an idea of the strength of the opposing induced emf produced, when the magnetic flux is changed by changing the rate of current flow in the same circuit . Every circuit loop has some inductance. When the circuit contains coils with many turns there could a significant inductance and the coil could be called an inductor. Inductors gives high frequency currents a hard time to pass through. Lower frequency AC pass through with more ease. Steady currents (DC) have no problem passing through inductors. In technical terms we say, Inductors show reactance(XL) to high frequency currents, since they react against higher frequency current the most. Capacitors behave exactly opposite to Inductors. Capacitors dont react against higher frequencies much, while low frequency currents have hard time passing through the capacitor due to its high reactance (XC).
- 13. Supplemental study guide PHYS II In an RLC circuit we have both Inductor (L) and Capacitor(C). The C can deny frequencies below a certain value while the L can deny frequencies above a certain value of frequency. Hence, RLC circuit are said to exhibit resonance. Resonance here refers to the fact that the RLC circuit will only allow certain frequencies. All frequencies below them are denied by C and all the other frequencies above them are denied by the L.
- 14. Supplemental study guide PHYS II The first equation says that the electric flux out through a closed surface will be proportional to the charge Q that surface encloses. The second equation says that the magnetic flux out through a closed surface will always be zero, since the surface can never enclose a magnetic charge as there doesn’t exist such a thing as magnetic charge or a magnetic monopole. The third equation says if there is change in magnetic flux through any open surface, there would an induced emf calculated by summing up all E.dS (remember Ed = V) along the total perimeter of that open surface. The fourth equation says if there is current penetrating through any open surface or change in electric flux through that open surface it would result in a magnetic field along the boundary of the open surface, which would be a closed curve (loop), such that the above equation is satisfied. The last 2 laws suggest the existence of a self-sustaining Electromagnetic wave which can exist only if it travels at a speed c. Visible light is part of the frequency spectrum of Electromagnetic waves.