15 marks Consider a model of a spherical cell of radius r. The interior of the cell we will model as a conducting sphere of radius ra. This is separated by a lipid layer of thickness a and dielectric constant K from the exterior of the cell which we will also model as a perfect conductor. The interior of the cell is negatively charged. With these assumptions use Gauss's law to determine the capacitance of the cell. Follow the following steps, that correspond to what we did in class for the parallel plate capacitor (a) Suppose there is a charge -Q on the cell. Argue that the electric field must be spherically symmetric. (b) Use Gauss's law for a material with dielectric constant K to find the electric field in the cell membrane (c) Use the definition of electric potential to find the potential difference across the cell membrane (d) Use the definition of capacitance to find the capcitance from the electric potential