Two spherical conductors of radii R1 and R2 are separated by a distance much larger than the radius of either sphere. The spheres are connected by a conducting wire as shown in figure. If the charges on the spheres in equilibrium are q1 and q2, respectively, what is the ratio of the field strength at the surfaces of the spheres?

Question

Two spherical conductors of radii R1 and R2 are separated by a distance much larger than the radius of either sphere. The spheres are connected by a conducting wire as shown in figure. If the charges on the spheres in equilibrium are q1 and q2, respectively, what is the ratio of the field strength at the surfaces of the spheres? (A) R2 / R1 (B) R22 / R12 (C) R1 / R2 (D) R12 / R22

Tardigrade Admin · Accepted Answer

Their potential will be same, i.e., V1=V2 or (k q1/R1)=(k q2/R2) or (q1/q2)=(R1/R2) or (E1/E2)=(k q1 / R12/k q2 / R22)=(q1/q2)((R2/R1))2 =(R1/R2)((R2/R1))2=(R2/R1)

$R_{2} / R_{1}$

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

$R_{1} / R_{2}$

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

R2​/R1​

R22​/R12​

R1​/R2​

R12​/R22​

Their potential will be same, i.e., V1​=V2​ or R1​kq1​​=R2​kq2​​ or q2​q1​​=R2​R1​​ or E2​E1​​=kq2​/R22​kq1​/R12​​=q2​q1​​(R1​R2​​)2 =R2​R1​​(R1​R2​​)2=R1​R2​​

$R_{2} / R_{1}$

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

$R_{1} / R_{2}$

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