Question

Its plate area is 1.0 cm:, the plate separation is 8.85 mum Show the capacitance Cj is 1.0 x 10 F when filled with air. Find electric field j^j between the plates of C_j assuming the surface charge density is 3.0 muC/n?. Calculate the voltage across the plates of C_j assuming surface charge density is 3.0 muC/m^2. Show' by unit analysis that C/F = V. Styrofoam-filled plates (k = 2.1) of C_3 are compared to air-filled parallel plates of Cj: by calculation we conclude: AV to [be smaller, be larger, stay the samel across the insulator filled plates when Q remains the same.

Answer 1

Capacitance, CCCC 8x101°F, C3 Area of the plate. A 1x 10-4 m2 1x10-1 F Consider the first loop, Here C1 and C are parallel Effective capacitance, C+C a. =8x10-10 +8x10-10 1.6x10-9F Consi der the second loop, C4 andC are par allel -8x10-10 +8x10-10 = 1.6×10-19F For parallel plate capacitor Aeok (A = area of plates, d = distance of seperation k = relative permittivity 1оґ x 8.85 x 10-12 x 1 8.85×10-6 =110-10F

b. Electric field (suface charge density) σ=2 (0-charge) From Gauss law, If an oppositely charged plate is placed to form a parallel plate capacitor, Thus, Eins - 3x10-5 8.85x10 3.39x103N/C c. Wehave the relation,

Voltage,V- eo 3x10-5x8.85x10 -008 10-12 8.85x10 -3 V d. Using the relation, Voltage, From unit analysis, (permittivity of free space, 8.85x10-F/m V-Hence proved