Question

Two conducting spheres of radii r₁ and r₂ are equally charged. The ratio of their potentials is
(a) $\frac{r_{1}}{r_{2}}$
(b) $\frac{r_{2}}{r_{1}}$
(c) $\frac{r^{2}_{1}}{r^{2}_{2}}$
(d) $\frac{r^{2}_{2}}{r^{2}_{1}}$

Answer 1

the answer is[ tex/] frac {r _{1}}{r _{2}}[/tex]

Answer 2

Answer:

B) r₂/r₁

Explanation:

Capacitance of first sphere , C₁ = 4πε₀r₁

Capacitance of second sphere , C₂ = 4πε₀r₂

Let final potential = V

After connecting, the transfer of charge from a higher potential sphere to lower potential sphere and finally, potential of both sphere will be equal

Charge at first sphere, Q₁= C₁V = 4πε₀r₁V

Charge at second sphere ,Q₂ = C₂V = 4πε₀r₂V

Thus, ratio of charge = Q₁/Q₂= 4πε₀r₁V/4πε₀r₂

V = r₁/r₂ -- (1)

Ratio of electric field = E₁/E₂ = KQ₁/r₁²/KQ₂/r₂²

= Q₁r₂²/Q₂r₁²

E₁/E₂ = (Q₁/Q₂)(r₂²/r₁²)

Put equation (1)

E₁/E₂ = r₂/r₁

Hence, the ratio of the potential is r₂ : r₁