Physics MRI Essay Example | Topics and Well Written Essays - 1000 words

Physics MRI - Essay Example The Larmor (or resonant) frequency ω0 is the frequency at which the nuclide precesses about the magnetic field. The resonant frequency is equal to the magnetogyric ratio ÃŽ ³ (specific to the nuclide) times the magnetic field B (Brandolini, 2004): the nuclide 13C at 75 MHz. From the equation above, the magnetogyric ratio ÃŽ ³ is constant so that ÃŽ ³ =ω0 /B = ω’0 /B’, where ω’0 is the resonant frequency when the magnetic field B’ = 1.5 T. Solving for ω’0 : ω’0 = (ω0 B’)/B what is the mean B and B This is explained in the sentence directly above: the single prime corresponds to the resonant frequency when the magnetic field is 1.5 T. You are asking what is meant by B’, but if you look at the sentence above, it was just defined: B’ = 1.5T. It is the magnetic field at 1.5T. B’’ is just a different value of the magnetic field (in this case 4 T) where we are trying to find the frequency w0’’ that corresponds to it. From this equation, if you know the frequency ω0 and the magnetic field B, then the ratio of these is the gyromagnetic ratio. We know the frequency at 6.9T from the reference cited above. Therefore, to find the frequency at a different magnetic field, we just use the equation w0/B = ÃŽ ³ = constant. So another set of corresponding values of w0 and B, call these new values w0’’ and B’’, will also have the same ratio: w0’’/B’’ =ÃŽ ³ constant = w0/B. Since we now have w0’’/B’’ = w0/B, we can multiply both sides by B’’ to get: w0’’ = w0 * B’’/B . Hopefully you can now see where that equation comes from. The reason I didn’t put the calculation down in this case, is because it is EXACTLY the same as the calculation before it, but with different values. You can just follow the equations that were used in the example above it, putting in the

Market equilibrium Research Paper Example | Topics and Well Written Essays - 750 words

Market equilibrium - Research Paper Example Production and consumption of goods and services are influenced by several factors. However, it is worth to note that there are critical aspects of the society that determines demand and supply. In the context of economics, the society is always entangled in a struggle to satisfy its diverse needs with limited resources. Exchange of goods and services constitutes market and is subject to natural or artificial forces (Dwivedi,2010). The goal of the society has remained achieving equilibrium in the market. In other words, market equilibrium is a state of balance between goods and services supplied and demanded. Under this condition prices and quantity are reconciled between the seller and the buyer. For instance, assuming the equilibrium price is Pe and equilibrium quantity is Qe;it mean that the seller and the buyer has consented the quantity and prices. A diagrammatical presentation of a market equilibrium can be shown below.Supply and demand curves.(Fig.1)The figure .1 above shows t he supply and demand curves with the convergent points indicating equilibrium. This Pe represents equilibrium price and Qe representing equilibrium quantity. It is worth to note that the highlighted prices and quantity stated are mutually accepted by the two parties to the agreement. In other words, there are times when the demand and supply of goods shows no tendency to change and this constitutes market equilibrium. The price changes are a function of equilibrium status of the market.