Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1 (on S2) and E2(on S2) on their surfaces are such that E1/E2 = R1/R2. Then the ratio V1(on S1)/V2(on S2) of the electrostatic potentials on each sphere is :

Question

Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1 (on S2) and E2(on S2) on their surfaces are such that E1/E2 = R1/R2. Then the ratio V1(on S1)/V2(on S2) of the electrostatic potentials on each sphere is : (A) ((R1/R2))3 (B) (R2/R1) (C) R1/R2 (D) (R1/R2)2

Tardigrade Admin · Accepted Answer

E1=(KQ1/R21) E2=(KQ2/R22) Given, (E1/E2)=(R1/R2) ((KQ1/R21)/(KQ2)R22)=(R1/R2) ⇒ (Q1/Q2)=(R31/R33) (V1/V2)=(KQ1/ R1/KQ2 / R2)=(R21/R22)

$(\frac{R _{1}}{R _{2}})^{3}$

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

$R_{1} / R_{2}$

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

(R2​R1​​)3

(R2​/R1​)

R1​/R2​

(R1​/R2​)2

E1​=R12​KQ1​​E2​=R22​KQ2​​ Given, E2​E1​​=R2​R1​​ R22​KQ2​​R12​KQ1​​​=R2​R1​​⇒Q2​Q1​​=R33​R13​​ V2​V1​​=KQ2​/R2​KQ1​/R1​​=R22​R12​​

$(\frac{R _{1}}{R _{2}})^{3}$

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

$R_{1} / R_{2}$

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