4)Consider a charge +q, located at the origin. We observe the potential V and the electric field E at distance r. Here w

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4 Consider A Charge Q Located At The Origin We Observe The Potential V And The Electric Field E At Distance R Here W 1 (793.97 KiB) Viewed 230 times

4)Consider a charge +q, located at the origin. We observe the potential V and the electric field E at distance r. Here we are interested in quantities along the z-axis. Find or, if you know it, simply write, the electric potential V along the z-axis (x =y=0), for [z| not equal to zero. (Izis the absolute value of z.) Can you make any arguments by symmetry about the electric field? For instance, are any components of the electric field equal to zero along the z-axis? Use the standard expression, E; = -av/axi, where the E; are the x, y, z components of E, and Xi refer to the coordinates x, y, z. Using the expression you found above for V, what is the vector E as a function of position along the positive z-axis (lz| not equal zero). = Recall the differential form of Gauss' law, V. E=p/€0. What does this say about the component Ex at points Ax away from the z-axis, as a function of z? -