uupuinLAA uniformly charged segment of line charge of length Lis placed on the z
ID: 2079599 • Letter: U
Question
uupuinLAA uniformly charged segment of line charge of length Lis placed on the z-axis in free space as shown in Fig. I.The line charge density is pu. Assume pu is positive. (a) point) What is the most appropriate coordinate system to use for solving this problem? (b) (1 point By symmetry, what is the direction of the electric field produced by this charge at any point in the x planc? Why? (c) (5 points) Find the electric field (magnitude and direction) produced by this charge in the x-y plane as a function of the distance to the line segment. Express your answer in terms Fig. l of pu. L. go, unit vectors of an appropriate coordinate system, and anything else you may need. Hint: the following integral may be useful (a +x Now consider the new charge configuration: asquare of line charge in the xy plane as shown in Fig. 2. The line charge density is pu. (d) point) By symmetry, what is the direction of the electric field produced by this charge at points on z axis? Why? (e) points) Find the electric field (magnitude and direction) produced by this new charge configuration on z-axis as a function of the z-coordinate. Assume pu is positive. Express your answer L/2 in terms of pu. ge, unit vectors of an appropriate coordinate system, and anything else you may need. L/2 Fig. 2 Solution: (a) cylindrical coordinates b) The direction of the electric field in the x-y plane should be a .The line charge is not only mirror symmetric in x-y plan but also rotation symmetric along z axis. (c) See the graph below dE Since the component along a direction is an odd function of z, it will be cancelled out after we apply an integral from-L2 to LU2 with respect to z. So, we only need to care about the component along a direction. dEExplanation / Answer
It is very simple.As P(row) is the distance between observation point and the line charge,as per the pythogarus theorem hypotenuse=(sum of squares of sides in perpendicular) I.e.,p2=((L/2)^2+z^2)=(L^2/4+z^2)
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