Two charged spheres of radii R1 and R2 have equal surface charge density. The ratio of their potential is

Question

Two charged spheres of radii R1 and R2 have equal surface charge density. The ratio of their potential is (A)  R1/ R2 (B)  R2/ R1 (C)  (R1/ R2)2 (D)  (R2/ R1)2

Tardigrade Admin · Accepted Answer

Given two spheres of radii R 1 and R 2 have equal surface charge density. To find the ratio of their potentials at an equidistant external point. Let us suppose that the sphere with radius R 1 has charge q 1 on it, and that the sphere with radius R 2 has a charge q 2 on it. Now, they have same charge densities, so ( q 1/4 π R 1 2)=( q 2/4 π R 2 2) So, ( q 1/ q 2)=(( R 1/ R 2))2 ...(i) Potential in first sphere, V 1=( k q 1/ R 1) Potential in second sphere, V 2=( kq / R 2) Thus, ( V 1/ V 2)=( q 1/ R 1) ⋅ ( R 2/ q 2) =( q 1/ q 2)(( R 1/ R 2))2 From (i), (V1/V2)=((R1/R2))2 × (R1/R2)=(R1/R2)

Q. Two charged spheres of radii $R_{1} an d R_{2}$ have equal surface charge density. The ratio of their potential is

$R_{1} / R_{2}$

$R_{2} / R_{1}$

$(R_{1} / R_{2})^{2}$

$(R_{2} / R_{1})^{2}$

Q. Two charged spheres of radii R1​andR2​ have equal surface charge density. The ratio of their potential is

R1​/R2​

R2​/R1​

(R1​/R2​)2

(R2​/R1​)2

Q. Two charged spheres of radii $R_{1} an d R_{2}$ have equal surface charge density. The ratio of their potential is

$R_{1} / R_{2}$

$R_{2} / R_{1}$

$(R_{1} / R_{2})^{2}$

$(R_{2} / R_{1})^{2}$