TEST III. PROBLEM SOLVING. Solve the following problems. Show your solutions clearly and box your final answer in the solution. (5 points each) NOTE: Final answer must be in decimal form; 4 decimal places) 1. A given electrostatic force is expressed as? = pz sin P a? + 3p cos @ a? + p cos @ sin @ a? - Since vector form of electrostatic force can be expressed in other coordinate systems, you are required to convert this vector force into Cartesian coordinates. What is the resulting vector form? 2. A Lasallian Electronics engineering is now working as a scientist for one of the leading institution studying electromagnetism. This Lasallian engineer is currently studying a vector field expressed as = ?12 cos ? a?+ 72 sin ? cos? a?+ 2 cos ? a? . Since he is currently very busy in other tasks, he asked for your help in solving for the divergence of this vector field. What is the divergence of this vector field? 3. One of your ECE friend identified two point charges QA = 250 uC located at (5,2,0) m and QB = - 300 HIC located at (2,0,-5) m. Since you are now an expert in electrostatics, this friend of yours asked for your help to determine the force on QB due to QA . Find that force in cartesian vector form? 4. There is a volume defined by 1 s ?