A spherical capacitor formula is given below: Where, C = Capacitance Q = Charge V = Voltage r 1 = inner radius r 2 = outer radius ε 0 = Permittivity (8.85 x 10 -12 F/m) See the video below to learn problems on capacitors. Hope you learned the spherical capacitor formula.
Two concentric spherical conducting shells are separated by vacuum. The inner shell has total charge +Q and outer radius , and outer shell has charge -Q and inner radius . Find the capacitance of the spherical capacitor. Consider a sphere with radius r between the two spheres and concentric with them as Gaussian surface. From Gauss’s Law,
As mentioned earlier capacitance occurs when there is a separation between the two plates. So for constructing a spherical capacitor we take a hollow sphere such that the inner surface is positively charged and the outer surface of the sphere is negatively charged. The inner radius of the sphere is r and the outer radius is given by R.
For more such interesting formulas and concepts subscribe BYJU’S YouTube Channel!! The capacitance of the Spherical Capacitor is found by analysing the voltage difference between the conductors for a given charge on each, It also depends on the inner and outer radius of each sphere.
Solution: C = 4 πεox F C = 4 × 3.14 × 8.85 × 10−12 × 10 × 10−2 C = 111.156 × 10−13 C = 1.11 × 10−11 F Now Q = CV Therefore Hence V = 900.9 V Question 5: The outer radius of a spherical capacitor is 10 % bigger than its inner radius.
C = 4 π ϵ 0 (1 R 1 − 1 R 2) − 1. It is interesting to note that you can get capacitance of a single spherical conductor from this formula by taking the radius of the outer shell to infinity, R2 → ∞. R 2 → ∞. Since we will have only one sphere, let us denote its radius by R. R. C single sphere = 4πϵ0R. C single sphere = 4 π ϵ 0 R.