Three concentric spherical shells have radii a, b and c

Three concentric spherical shells have radii a, b and c (a < b < c) and have surface charge densities, σ, – σ and σ respectively. If V_A, V_B and V_C denotes the potentials of the three shells, then for c = a + b, we have

c = a + b.

V_A =	σ_a	-	σ_b	+	σ_c	=	σ	[c - (b -a)]
	ε₀		ε₀		ε₀		ε₀

V_B =	σ_c	-	1	.	σ × 4πb²	+	1	.	σ × 4πa²
	ε₀		4πε₀		c		4πε₀		c

=	σ		c -	(b² - a²)
	ε₀			c

=	σ	[c - (b - a)]
	ε₀

V_A = V_CB