# Problems2_2010 - =2r 1 carries net charge of Q At the...

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Physics 205, Electricity and magnetism. 2010, Problem set #2. Hints: I am wondering how well you can integrate… And if you still remember the material of previous paragraphs… As well as the examples we considered in class. 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. 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 units 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. Problem 3. A hollow spherical conductor with inner radius r 1 and outer radius r 2
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Unformatted text preview: =2r 1 carries net charge of +Q. At the center of the sphere is a point charge +Q/2. Find the electric field strength and potential in three regions: a) r<r 1 , b) r 1 <r<r 2 and c) r>r 2 . Plot E(r) and V(r). Problem 4. The HCl molecule has a dipole moment of about 3.4x10-30 C . m. The two atoms are separated by about 1 . 10-10 m. What is the net charge on each atom? Comment on the numerical value of that charge. What is maximal torque that this dipole will experience in a 2.5 . 10 4 N/C electric field? How much energy one would need to rotate one molecule 45 o from its equilibrium orientation? Problem 5. An isolated charged parallel-plate capacitor with the plate separation d=1 mm and area of A=10 cm 2 is initially empty. One slides a polystyrene dielectric slab with thickness equal to half the plate separation and with only half the area of the plates into the region between the plates. What is the final capacitance?...
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