Given a square of side a, lying in the x-y plane, with one corner at the...

Given a square of side a, lying in the x-y plane, with one corner at the origin and the two adjacent sides aligned with the x and y axis, respectively. Three of the corners of the square are occupied by fixed charges: two equal positive charges Q each at (a,0) and (0.a), and a negative charge -q at (a,a). There is NO charge at the origin (0.0). We want to find and discuss the NET electric field AT THE ORIGIN (call it E) due to the three given charges. Let’s do that step by step--

(a) Sketch the setup.
(b) State what the DIRECTION of E must be, no matter what the values of Q and q. No calculation

required but give a convincing argument.
(c) Now calculate E. (Remember, E is a vector!) Simplify your result by collecting all the x

components and all the y components, and factoring out common factors.
(d) For given Q what must be q such that E is zero? Give your answer in the form, q = c Q, where c

is a NUMERICAL factor (like 1/5 or 2sqrt(2) or the like). Hint: careful inspection of your answer to part (c) will save you a new calculation!

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Expert Solution

genius_generous answered 1 year ago

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