Please answer and show the work on the following PHYS short answer questions

l) (10 Points) On its mission to explore the UNIVERSE, the USS Enterprise ( m E = 100,000 [kg] ) discovers an innite length rod in an otherwise empty region of space. The captain decides to send out a probe to study the properties of the rod. The Enterprise \"parks\" 200 [km] from the rod, holding itself at rest relative to the rod by applying a constant thrust force away 'om the rod with a magnitude of 1 [MN] (1 [MIN] = 1,000,000 Newtons). It then res out a \"probe" which is effectively a bowling ball with a mass m B: 20 [kg ] and charge q B = + 5 [H.C] . The \"probe" moves about the rod in a circular orbit with speed 15,000 [m/s]. :1) Draw a FBD of the (uncharged) Enterprise at rest near the rod. 2ka r b) Find the linear mass density A," of the rod. Note: 3: 1:) Draw a FBD of the orbiting bowling ball \"probe" d) Find the linear charge density kg 2) (10 Points) A 2D annulus (thick ring) has an inner radius R,- and outer radius R0 , and charge Q nan-uniformly distributed over its surface. The 2D charge density varies with radius r by 7] (r): (ft-4 for Rig rSRa and n=0 for all other r. C is a constant. Answer the following in terms of the variables given above. Note: Gauss' Law will not be useful here. 3!) Find an expression for C such that the total charge of the annulus is Q. include the SI units for C next to your answer. Do the units make sense? b) Draw a clear picture and use it to set up the integral to calculate the E-eld at a point on the axis of the annulus (this axis is perpendicular to the plane of the annulus) a distance 2 'om the center of the annulus. *** You must complete all the steps short of actually computing the integral (i.e. your nal answer mint be an integral with only ONE variable of integration and all other variables constant.) Show that your answer has the correct SI units for the electric eld. 3) (10 Points) Four point charges are held xed in space on the comers of a rectangle with a length of 20 [cm] (in the horizontal direction) and a width of 10 [cm] (in the vertiwl direction). Starting with the top le comer and going clockwise, thechargesare q|=+10[nC] 1 qz=10[nC] 1 q3=5[nC] 1aDd q4=+8[nC] - :1) Find the magnitude and direction of the electric force on charge q4 b) Find the magnitude and direction of the electric eld at the point between q 3 and q, 1:) Find the magnitude and direction of the electric eld at the center of the rectangle