For problems 3 &4, a Newton-Raphson Matlab code (NR.m) is available for you to use in solving the problems. If you use the code as is, there is no need to submit any Matlab code. Remember an empty vector can be easily represented as [] and if you do not want the program to show calculation steps or a plot enter a zero,"0. However, if you edit NR.m or create any new .m files, you must submit with your work to receive full credit. 3. Magnetic resonance imaging (MRI) is a rapidly advancing area of biomedical imaging. MRI interrogates the nuclear environment of hydrogen protons in the soft tissues of the body providing contrast imaging as well as functional imaging of tissues. A common coil used for MRI experiments is the solenoid. A solenoid coil can be used to couple energy into a sample and to detect the time-varying magnetic flux density during the acquisition of signals. The solenoid has length and radius a. The long axis of the solenoid is along the y-axis. The solenoid produces a flux density at any observation point y, which depends on the number of turns in the coil, N, the amount of current, and po, the permeability of free space, which is typically 4TT x 10-7H/m. The inductance of a coiled solenoid is given approximately as + a Compute, using Newton-Raphson method in MATLAB, the radius of the solenoid coil, a, to provide inductance of 2.6 uH, assuming the following parameters N 10 turns 1-20 cm Plot the function and the path to the root in Matlab (Hint: Use TRACE-2). Annotate the graph to explain what happens and comment on what happens if you change the original guess For problems 3 &4, a Newton-Raphson Matlab code (NR.m) is available for you to use in solving the problems. If you use the code as is, there is no need to submit any Matlab code. Remember an empty vector can be easily represented as [] and if you do not want the program to show calculation steps or a plot enter a zero,"0. However, if you edit NR.m or create any new .m files, you must submit with your work to receive full credit. 3. Magnetic resonance imaging (MRI) is a rapidly advancing area of biomedical imaging. MRI interrogates the nuclear environment of hydrogen protons in the soft tissues of the body providing contrast imaging as well as functional imaging of tissues. A common coil used for MRI experiments is the solenoid. A solenoid coil can be used to couple energy into a sample and to detect the time-varying magnetic flux density during the acquisition of signals. The solenoid has length and radius a. The long axis of the solenoid is along the y-axis. The solenoid produces a flux density at any observation point y, which depends on the number of turns in the coil, N, the amount of current, and po, the permeability of free space, which is typically 4TT x 10-7H/m. The inductance of a coiled solenoid is given approximately as + a Compute, using Newton-Raphson method in MATLAB, the radius of the solenoid coil, a, to provide inductance of 2.6 uH, assuming the following parameters N 10 turns 1-20 cm Plot the function and the path to the root in Matlab (Hint: Use TRACE-2). Annotate the graph to explain what happens and comment on what happens if you change the original guess