Question

B: ANSWER ONLY ONE (1) QUESTION ON 5 120 MARKS gure 3 shows a spherical type capacitor used to measure the volume of liquids, consists of wo spherical shells where the inner and outer radii given by a and b, respectively are Find the electric field E in the region a <r<bif the total charge on the surface ra is given by O 15 Marks C81, PO, 62 (ii) Express the potential difference V between r Derive the capacitance of the capacitor. a and r b () Find the surface charge density pa on the surface r a if the potential difference between these shells is given by 10V. Write your final answer in terms of a and b (Hint: Q- fp.dS= CV) (iv) [10 Marks , , Investigate the ratio change of capacitance before and after the capacitor is fully immersed into the liquid (see Figure 3(b). Given that the electrical relative permittivity of the liquid is E4, and the relative permittivity outside the liquid is , 1. Show all related calculations. [5 Marks (b) 10v (a) 10V Figure 3 (a) A spherical capacitor. (b) The spherical capacitor is fully immersed in the liquid.

electromagnetic fields theory

Answer 1

Radius of înner and outer Shells are a&b. Tesp... fns (i) total charge Cn suyface T =a is @. Apply Giauss law to an arbitrary Gaussian Spherial Suy face af Tadius e E as E Ev. (UTT) E-permittivity of medium. E = where Electric field for arb (VIm) ar UTTEY (it) potential difference V: ar (dT ay) ha E.dl Q b uTET dr a for aYb - UTTEY ci capacitance C G ohere V = V = t-1/ (F) betueen a&b. UTTE utrE - V capacitance c = utTE i) Q Ps ds = cv Where fs.aPs ,V=l0 V at y=a JPsa ds ID (UTS) Ps.a ds = Ps,a (uTa) (b/a) (b-a) 10E 102 10 (uTE) aT 4-1 suface charge density fs a uITa ab = 108 (6 la) Cl (b-a) Say Cis befove and c is after capacitances. (En &Er2= 4) CL Co E So Ca E2 Ca. *The ratio ot change ot Capacitances C C2