3 Physics problems

1) In the figure the battery has potential difference V = 13.5 V, C₂ = 3.30 μF, C₄ = 3.80 μF, and all the capacitors are initially uncharged. When switch S is closed, a total charge of 11.0 μC passes through point a and a total charge of 9.00 μC passes through point b. What are (a) C₁ and (b) C₃?

2) The figure shows a parallel-plate capacitor with a plate area A = 6.69 cm² and plate separation d = 9.90 mm. The left half of the gap is filled with material of dielectric constant κ₁ = 5.80; the right half is filled with material of dielectric constant κ₂ = 14.7. What is the capacitance?

3) A certain cylindrical wire carries current. We draw a circle of radius r around its central axis in Figure (a) to determine the current i within the circle. Figure (b) shows current i as a function of r². The vertical scale is set by i_s = 5.3 mA, and the horizontal scale is set by r_s² = 4.6 mm². (a) Is the current density uniform? (b) If so, what is its magnitude?

Figures are uploaded for the three questions. Please include the unit for each answer.