Physics 208: Electricity and Magnetism Exam 1, Secs Feb IMPORTANT. Read these directions carefully:

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1 Physics 208: Electricity nd Mgnetism Exm 1, Secs Feb Instructor: Dr. George R. Welch, 415 Engineering-Physics, Print your nme netly: Lst nme: First nme: Sign your nme: Plese fill in your Student ID number: IMPORTANT Red these directions crefully: There re 5 problems totlling 100 points. Check your exm to mke sure you hve ll the pges. Work ech problem on the pge the problem is on. You my use the bck. If you need extr pges, I hve plenty up front. Indicte wht you re doing! We cnnot give full credit for merely writing down the nswer. Netness counts! I will give generous prtil credit if I cn tell tht you re on the right trck. This mens you must be net nd orgnized. Ech problem with its ssocited figure is self explntory. If you must sk question, then come to the front, being s discrete s possible so s not to disturb others. Put your nme on ech pge it is sked for. You will lose credit if you fil to print your nme on ech pge it is sked for.

2 Print your nme: Physics 208: Electricity nd Mgnetism, Exm 1 Problem points. Two chrged prticles re seprted by distnce. One prticle hs chrge Q nd the other hs chrge +2 2 Q. Consider the point P shown by n in the Figure. Point P lies on line perpendiculr to the line connecting the two chrges, nd distnce from the negtive chrge. Using the coordinte system shown, clculte the x- nd y-components of the electric field t point P. Note: but you re not to use this pproximte deciml expression. Solve the problem exctly. Hint: cos 45 = sin 45 = 1/ 2. +y P +x You need to be net! Sty orgnized nd indicte wht you re doing.

3 Print your nme: Physics 208: Electricity nd Mgnetism, Exm 1 Problem points. A long cylindricl rod of rdius R crries chrge per unit length λ tht is uniformly distributed throughout the rod. () (2 points) Why is ρ = λ πr? Just one sentence! 2 Suppose the rod to be infinitely long. Then the electric field points rdilly outwrd. Clculte the electric field distnce r from the center of the rod for the following two cses: (b) (10 points) r R. (c) (13 points) r R. λ R Be net. Netness help.

4 Print your nme: Physics 208: Electricity nd Mgnetism, Exm 1 Problem points. A thin rod of length L crries totl chrge Q tht is uniformly distributed long its length. Consider the point P shown by n in the Figure. Point P lies long the line of the rod nd distnce from one end. () Clculte the electric field t point P. (b) Clculte the electric potentil t point P ssuming tht the potentil is zero infinitely fr wy. Q P L Don t forget to be net.

5 Print your nme: Physics 208: Electricity nd Mgnetism, Exm 1 Problem points. A lrge flt slb of nonconducting mteril crries uniform chrge per unit volume ρ. The thickness of the slb is d nd is is not negligible. The Figure shows cross section through the slb. The x-xis is perpendiculr to the slb, nd we tke x = 0 to be t the center of the slb. Outside the slb, the electric field points perpendiculrly wy from the slb. In clss nd in the book we used Guss lw to show tht its mgnitude is given by by E = ρd 2ɛ 0 for x d 2. (1) Inside the slb, the electric field is zero t the center, nd increses s you go out. It it is given E(x) = ρx ɛ 0 for x d 2. (2) This expression is positive for x > 0 nd negtive for x < 0 which mens the electric field points in the +x-direction for x > 0 nd in the x-direction for x < 0. Derive n expression for the electric potentil inside the slb. potentil to be zero t x = 0. As reference, tke electric ρ d x = 0 x Remember, more points if you re net.

6 Print your nme: Physics 208: Electricity nd Mgnetism, Exm 1 Problem points. Three prticles re rrnged on line. The middle prticle hs chrge Q nd the two outer prticles ech hve chrge +2Q. Ech of the two outer chrges re the sme distnce from the center chrge. Clculte the electrosttic potentil energy stored in this system of chrges. I cn grde your work more generously if I cn red it! Be NEAT!