(Solved): 1.) [1.5 pt] Determine the electric field at the middle of the square of side length a shown in th ...

1.) [1.5 pt] Determine the electric field at the middle of the square of side length $$a$$ shown in the diagram. The four charged particles at the corners of this square each have the same amount of charge; however the two particles on the left side are positive, while the two on the right side are negative. 2.) [1.5 pt] Two charged particles are located on the $$x$$ axis as shown in the diagram. Determine the total electric field due to these particles (a) at location $$\mathrm{A}$$ and (b) at location B. 3.) [2 pt] A negative charge $$?Q$$ is spread out evenly along the circular arc of radius $$a$$ shown in the diagram. Determine an expression for the electric field at the origin. Express your answer in terms of the unit vectors $$\hat{\mathbf{i}}$$ and $$\hat{\mathbf{j}}$$. You may find it helpful to use an angle as the variable of integration.