A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm . The outer sphere is earthed and the inner sphere is given a charge of 2.5 μ C. The space between the concentric spheres is filled with a liquid of dielectric constant 32 . The capacitance of the capacitor is

Question

A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm . The outer sphere is earthed and the inner sphere is given a charge of 2.5 μ C. The space between the concentric spheres is filled with a liquid of dielectric constant 32 . The capacitance of the capacitor is (A) 5.5 × 10-9 F (B) 6.5 × 10-9 F (C) 7.5 × 10-9 F (D) 8.5 × 10-9 F

Tardigrade Admin · Accepted Answer

Here, ra=12 cm =12 × 10-2 m rb=13 cm =13 × 10-2 m q=2.5 μ C =2.5 × 10-6 C , K=32 As C=4 π ε0 (K ra rb/rb-ra) =(1/9 × 109) (32 × 12 × 10-2 × 13 × 10-2/(13-12) × 10-2) =5.5 × 10-9 F

$5.5 \times 1 0^{- 9} F$

$6.5 \times 1 0^{- 9} F$

$7.5 \times 1 0^{- 9} F$

$8.5 \times 1 0^{- 9} F$

5.5×10−9F

6.5×10−9F

7.5×10−9F

8.5×10−9F

Here, ra​=12cm=12×10−2m rb​=13cm=13×10−2m q=2.5μC=2.5×10−6C,K=32 As C=4πε0​rb​−ra​Kra​rb​​ =9×1091​(13−12)×10−232×12×10−2×13×10−2​ =5.5×10−9F

$5.5 \times 1 0^{- 9} F$

$6.5 \times 1 0^{- 9} F$

$7.5 \times 1 0^{- 9} F$

$8.5 \times 1 0^{- 9} F$