Please answer the following 5 problems with work, reference pictures attached. Thank you!

\fProblem 1: Consider a conducting hollow cylinder. On the walls of the cylinder there is a uniform surface density of electric current g (see Figure 1). A conducting wire crosses the cylinder transversely. There is an electric current I in the wire. You are asked to calculate the absolute value of the magnetic field at a distance h from the wire at the point shown in Figure 1, which is on the axis of symmetry of the cylinder. Option A: 106 T Option B: 3 x 10-3 T Option C: 9 x 102 T Option D: 3.33 x 104 T Problem 2: Consider two electrically charged particles moving as shown in Figure 2. You are asked to calculate the velocity v such that the magnetic force that the two particles exert on each other is one quarter (1/4) of the electric force that the two particles exert on each other. Option A: 300,000.00 km/s Option B: 149,896.23 km/s Option C: 23,333.33 km/s Option D: 122.22 km/s Problem 3: Specify which of the configurations shown in Figure 3 satisfy the "action and reaction" law, Option A: a, b, d Option B: a, b, d Option C: a, b, c Option D: c, d Problem 4: Consider a capacitor like the one shown in Figure 4. Between the two parallel plates, there are two different dielectric materials, each occupying half the space between the plates. You are asked to: a) Calculate the capacity of this configuration. Option A: 88.121 mF Option B: 12.126 F Option C: 3.22 x 102 F Option D: 0.265 nF b) Now, suppose that the two dielectric materials are removed and the space between the plates is left empty. Calculate the capacity in that case. Option A: 88.54 10-12 F Option B: 0 Option C: 12.126 x 106 F Option D: 3.22 x 10-2 F Problem 5: Consider the circuit in the figure. V a) Calculate the current I. Option A: 4A Option B: 0.25 A Option C: 2A Option D: 1/3 A 0. 333 b) Calculate the current /1. Series . P. Option A: 0.33 A Option B: 4A Option C: 0.125 A Option D: 0.25 A