Please answer the following 5 problems with ALL work and formulas shown. Thank you!

Problem 1: Consider a sphere (i.e. empty sphere) of radius R=2m uniformly charged with surface charge density o = -0.995 x 10-1l C/m' (that is, =-0.00995 nC/m?); see Figure 1. Inside the sphere, at its center, lies a point-like particle of electric charge q=0.5 nC. You are asked to calculate: R = 1 Q = - 0.995 x 10-11 b) The acceleration experienced by the particle. a) The absolute value of the electric field at a point at a distance Im from the charge (i.e. from the Option A: 225.867 m/s2 Option B: 9.8 m/s2 Option C: -72.772 m/s2 Option D: 0 m/s2 center of the sphere). Problem 5: A solid cube of side L=2m uniformly charged (in volume) with an electric charge Option A: 4.493 N/C Option B: 12.122 N/C Option C: 0 N/C Option D: 3.333 N/C density p=8C/m' is enclosed by a spherical surface S; see Figure 5. You are asked to calculate: b) The absolute value of the electric field at a point at a distance of 6m from the center of the a) The flux of the electric field through the surface S. sphere. R = 6 Option A: 2.72x109 Nm-/C' Option B: 7.22x1012Nm /C Option C: 0 Option D: 3.22x1012Nm-/C Option A: 22.744 N/C Option B: 0 N/C Option C: 15.176 N/C Option D: 3.333 N/C b) The total electrical charge of this configuration. Option A: 4n C Option B: 8C Option C: 64C Option D: 6C Problem 2: Consider the configuration in Figure 2, with q=1 nC and L=2m. You are asked to b) The electric field in the center of the cube. calculate: Option A: 2.72 N/C Option B: 12.24 N/C Option C: 0 N/C Option D: 3.33 N/C ) The potential energy of the configuration. Figurel: Option A: 12.1 x 10-9 Nm ) Option B: -0.4 x 10-9 Nm Option C: 0.4 x 10-9 Nm ( Option D: 0 Nm 4 -b) The force on the charge that is located at the origin. Option A: -2.24x10-9N (itk) Option B: -2.24x10-N k Option C: 1.32x10-8N (itj) Option D: 0 Problem 3: Consider the configuration in Figure 3, with q=1 nC, L=2m, D=1m. You are asked to calculate: Figure 2: z (K) a) The electric field at the point P, located at a distance D=1m from the x axis. Option A: 0.003 N/C k Option B: 1.607 N/Ci Option C: -24.1 N/Ci Option D: 0 N/C Problem 4: Consider an infinite plane uniformly charged with superficial charge density o=2nC/m2. A particle with electric charge q=2x10"C and mass m=10-9Kg is placed at a distance above the plane. You are asked to calculate: 9 = 2 * 10 a) The electric field at the point where the particle is located. Option A: 12.427 N/C Option B: 112.933 N/C Option C: -12.993 N/C Option D: 7.29 N/C Figure 3: x (i) Figure 4 : Figure 5