In the figure below, each charged particle is located at one of the four vertices of a square with side length=a. In the figure, A= 3,8-2, and C-7, and g> 0. En Bq (a) What is the expression for the magnitude of the electric field in the upper right corner of the square (at the location of q)? (Use the following as necessary: a, a, and k.) 6.24k F- x Give the direction angle (in degrees counterclockwise from the +x-axis) of the electric field at this location. 45 X (counterclockwise from the +x-axis) (b) Determine the expression for the total electric force exerted on the charge q. (Enter the magnitude. Use the following as necessary: q, a, and K.) 6.24ka² Aye193.159, Fall 2032/Welln x Give the direction angle (in degrees counterclockwise from the +x-asis) of the electric force on q. 45 X(counterclockwise from the +x-axis)

A uniform electric field of magnitude 43.1N/C is parallel to the x axis. A circular loop of radius 25.7cm is centered at the origin with the normal to the loop pointing 27.4 above the x axis. A). Calculate the electric flux in, newton squared meters per coulomb, through the loop.  B).  To what angle, in degrees from the positive x axis, should the normal of the loop be rotated so that the flux through the loop becomes 0.419N⋅m2/C?

Give an expression for the electric field strength ?E at a point in terms of the charge ?q and distance ?r from the charge to that point. Use ?k for 14??014πε0 (i.e. ?≡14??0k≡14πε0).   Use the following notation (without the quotes): "/" for division,  "*" for multiplication, "+" an "-" as usual. For powers used "^2", while for square root use "sqrt". To indicate that square root applies to the whole expression use brackets - for example, for ??‾‾‾‾√AB use sqrt(A*B). For Greek letters such as ?π, ?α etc. use pi, alpha. For example to get 1??2???‾‾‾‾√1πA2BAB use 1/pi*A^2/B*sqrt(AB). Please use the exact variables given in the conditions of the problem: e.g if ?L is given, then do not use ?l.

Suppose you design an apparatus in which a uniformly charged disk of radius R is to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, at a point P at distance 2.60R from the disk (see Figure (a)). Cost analysis suggests that you switch to a ring of the same outer radius R but with inner radius R/2.60 (see Figure (b)). Assume that the ring will have the same surface charge density as the original disk. If you switch to the ring, by what part will you decrease the electric field magnitude at P? Number i Units (a) (b)