*Please show all working step by step with clarity! Charges +q. +2q. -5q and +2q
ID: 1916943 • Letter: #
Question
*Please show all working step by step with clarity!
Charges +q. +2q. -5q and +2q are placed at four corners ABCD respectively of a square of side a. The vector coordinates of A. B. C and D are: A = 0i + 0j, B = 0i + aj, C = ai + aj, D = ai + 0j respectively, where i and j are unit vectors. Determine the electric field strength Eo at the centre of the square (0 = a/2 i + a/2 j) via two methods described below, (i) and (ii). Express your answers in Cartesian components in terms of unit vectors i and j.Explanation / Answer
The diagonal of a square of 49.6cm on a side is sqrt(2)*49.6 = 70.14cm. The radial distance from the corner of the square to the center is half of this, or 49.6/sqrt(2) = 35.07cm. The two negative charges in quadrants II and IV are equal and opposite in electric field directions, so they cancel each other at the center of the square. The electric field of a point charge is Q/(4*pi*e*r^2), where "e" is the permittivity of free space, 8.854e-12f/m The positive charge produces a component of: 40*10^-6/(4*pi*8.854e-12*(.3507^2)) = 2.9227*10^6 V/m This component has an angle of 45 degrees, pointing into quadrant I. The negative charge produces a component with magnitude of: 26*10^-6/(4*pi*8.854e-12*(.3507^2)) = 1.8997*10^6 V/m This component also has an angle of 45 degrees, pointing into quadrant I, because of the negative charge. The resultant is the sum of the two components: E = 4.822*10^6 V/m, with an angle of 45 degrees in quadrant I.
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