A coil is wound twice around a rotor which is then placed in a uniform magnetic field having flux density of B = 1.7 T. The rotor is a cylinder

with a diameter of d = 155 mm. As shown in Figure 1, the coil that leads to Lorentz force, therefore,has four parts and they have the following features: All parts of the coil are perpendicular with each other. Each part of the coil that contributes to Lorentz force has a length of500 mm. The symbol x means the current is flowing into this document while the symbol •means the current is flowing out from this document. When the positions of all parts of the coil are as shown in Figure 1, the magnitude of the current flowing through all parts of the coil is (Qx 10) in A where Q has the value computed in Preamble. a) Calculate the magnitude of Lorentz force for each of the coil parts. b) Derive the expression for the net torque due to the Lorentz force for all the coil parts in terms of 0. You must show your working by copying or re-drawing Figure 1 in your answer script, and adding more sketches and labels on this figure to show how you derive this expression. c) Using the expression in Question 1b) and through differentiation method, find the value of 0 which leads to the maximum value of torque due to the Lorentz force. d) Calculate the net torque due to the Lorentz force for all the coil parts when0 = (Q × 100)° where Q has the value computed in Preamble. e) It is known that when 0 varies, there is a variation in the net torque due to the Lorentz force. Explain what modifications can be done to obtain more uniform torque as 0 varies. This could be either the arrangement of the coil or a change on an electrical quantity. f) Re-calculate the net torque due to the Lorentz force for all the coil parts if the magnetic field has been titled to the right by 10° as shown in Figure 2. 0 still has the value of (Q x 100)° where Q has the value computed in Preamble.You must show your working by copying or re-drawing Figure 2 in your answer script, and adding more sketches and labels on this figure to show how you obtain the answer.