Question

6. Consider a line charge with uniform charge density λ lying on the x-axis from z =-L to 0. a) Determine the electric field a distance y above the right end of the line charge (point P in the figure) and a distance r to the right of the line charge (point P2 in the figure). P2 b) In lecture you saw the electric field of an infinite line charge. Now we will consider a "semi-infinite" line charge; that is, a line charge that is infinite on only one side. In other words, suppose we take the left end of the line charge to be infinitely far to the left, but the line charge still stops at 0. What is the electric field at P and P2 in this case?

Answer 1

E-FIELD AT P_2 DUE TO dE vector E_2 = k dq/(X + X')^2 x dq = lambda dx', K = 1/4 pi epsilon_0 d vector E_2 = k lambda dx'/(x + x')^2 x vector E_2 = K lambda integral^0_-L dx'/(x + x')^2 x = -K lambda (1/x + x')^X' = 0_X' = -1 x = -k lambda (1/X - 1/X - L) x thatis (1) = -K lambda (x - L - K/X (X - L)) x = K lambda L/x (x - L) x vector E_2 = lambda L/4 pi epsilon_0 1/x (X - L) x E-FIELD AT P_1 DUE TO dq d vector E_1 = K dE/r^2 cos pi x + K dq/r^2 sin theta y = K lambda dX'/(x^2 + y^2)^3/2 x'/1 x + K lambda dx'/(x'^2 + y^2)^3/2 y y \r\n vector E_1 = K lambda integral^0_1 x' dx'/(x'^2 + y^2)^3/2 x + k Lambda y integral^0_X' = -L dx'/(x'^2 + y^2)^3/2 y = -K lambda (1/squareroot x^2 + y^2)^0_X' =

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