(a) Two particles of fixed negative charge -q are placed on a y axis at fixed positions of y = d and y = -d. (i) The electric field is probed at a point, P positioned at x = ad on the x-axis, where a is a variable. Illustrate and discuss the magnitudes and directions of electric field components at point P and also illustrate the net electric field at that point, of magnitude E. (ii) Starting from the expression for an electric field generated by a point charge, derive and simplify an expression for E in terms of a, q, d and any other constants required. (iii) Determine the magnitude of a that gives the maximum value of E. (iv) Sketch a graph for the electric field magnitude versus variable ‘a’, spanning positive and negative values of x, and label the maximum and minim values of E.
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