A spherical capacitor contains a solid spherical conductor ofradius 1mm, surroun

Question

A spherical capacitor contains a solid spherical conductor ofradius 1mm, surrounded by a dielectric materialwith r=2.0 out to a raiud of 2mm, then anouter thin spherical conducting shell. Determine the capacitance ofthe spereical capacitor. (HINT: Suppose you place a charge Q on theinner conductor and a charge -Q on the outer conductor. Determinethe electric field in the dielectric region between the conductors,then integrate E x dr to determine the voltagedifference between the conductors, and using the charge and thevoltage determine the capacitance of the spherical capacitor.)

Explanation / Answer

   Given          inner radiusof the capacitor    a = 1 mm =0.001   = 10-3 m          outer radiusof the capacitance   b = 2 mm = 0.002 = 2 * 10-3 m           dielectric constant     k   = 2.0           If wethen apply Gauss's Law for dielectrics on a spherical surface ofradius r, we have:                           2r2(K E + E) = Q/0 or E = [1/(20)] Q/(1+K)r2.               From this it easy follows Vab = 1/(20) Q/(1+K) (1/a - 1/b)                            and then C = 20 (1 + K) (a b)/(b -a).
   capacitance of a spherical capacitance withdielectric                      C = ( 1 / 2o ) [( k + 1 ) ( ab)   ] / (b - a )                           = ( 1 / 2 * 3.14*8.85 * 10-12 ) [ (2+1) (10-3 *2 * 10-3 )   /(0.002-0.001)                           =   0.1079 nF

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.