Question

Two concentric thin metallic spheres having radii 30 cm and 20 cm carry 10 µC and 5 µC, charges respectively. Calculate the electric potential at a distance of 25 cm from the centre of the spheres.

Answer 1

Let R₁ = 20cm = 0.2 m , R₂ = 30 cm = 0.3 m , r = 25 cm = 0.25 m
Q₂ = 10μC = 10 × 10⁻⁶ C = 10⁻⁵C , Q₁ = 5μC = 5 × 10⁻⁶ C

Now, by using Gauss theorem,
Electric potential at r = potential at r by sphere₁ + potential at r by sphere₂
potential at r by sphere₁ = KQ₁/r
Potential at r by sphere₂ = KQ₂/R₂ [ because potential be constant inside the sphere , here R₂ > r so, potential will be constant ]

Now, potential at 25 cm = KQ₁/r + KQ₂/R₂
Put all values ,
So, Potential at 25 cm = 9 × 10⁹ [5 × 10⁻⁶/0.25 + 10⁻⁵/0.3]
= 480 × 10³V = 480kV