A point charge of mass 0.210$\mathrm { kg }$ , and net charge $+ 0.340 \mu \mathrm { C }$ , hangs at rest at the end of an insulating cord above a large sheet of charge. The horizontal sheet of fixed uniform charge creates a uniform vertical electric field in the vicinity of the point charge. The tension in the cord is measured to be 5.18$\mathrm { N }$ . (a) Calculate the magnitude and direction of the electric field due to the sheet of charge (Fig. 79). (b) What is the surface charge density $\sigma \left( \mathrm { C } / \mathrm { m } ^ { 2 } \right)$ on the sheet?