Solutions2_2010

# Solutions2_2010 - Physics 205 Electricity and magnetism...

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Physics 205, Electricity and magnetism. 2010, Problem set #2. Problem 1: The electric potential of a very large isolated flat metal plate is 1000 V. The plate carries a uniform distribution of charge with surface density σ =10 μ C/m 2 . Determine potential V at a distance x=1 cm from the plate. Assume that point x is far from the edges and that x is much smaller than the size of the plate. The electric field can be calculated in the infinite plate approximation, since we are told that the plate is large and x is much smaller than the size of the plate 0 2 ε σ = E Potential difference: m C N V V C Nm Nm C m m C V d V V d Ed Eds V V A B B A A B ) / ( 4650 / 4650 / 10 85 . 8 2 01 . 0 / 10 1000 2 2 2 2 12 2 5 0 0 = - = - = - = - = - = - = - = - - - from V=Ed The negative answer is formally correct. However, I must admit that it does not look good, taking into account that intuitively the potential should reach zero at infinity. One could argue that I have chosen bad numbers for this problem However, no matter what numbers one chooses, if the plate is truly infinite, there always will be some distance, small compared to the infinite size of the plate, at which the potential will become negative… One could choose the numbers in such way that this issue gets unnoticed , but… In reality, any plate has finite size, and the potential changes linearly only in the very vicinity of the plate. At larger distances the dependence diverts from linear, and for distances much larger than the size of the plate it becomes ~1/ r, asymptotically approaching zero as it should do at infinity. 24 max A B 1 cm E

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Problem 2. The plastic rod of the length L=2 m has a non-uniform charge density λ =cx where positive constant c =5x10 -6 [some unit]. What unit c has to have? Find the electric potential at the point on the x axis 1 m to the left from the left end of the rod. Find the electric field at that point as well, via potential. First of all, λ is linear charge density, and the unit of it should be C/m. Therefore, c has to have unit of C/m 2 in order for cx to have units C/m. Here we assume that the point of interest is at the origin (x=0) and rod starts at
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Solutions2_2010 - Physics 205 Electricity and magnetism...

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