Two charged spherical conductors of radii R1 and R2 are connected by a wire. Then the ratio of surface charge densities of the spheres σ 1/σ 2 is

Question

Two charged spherical conductors of radii R1 and R2 are connected by a wire. Then the ratio of surface charge densities of the spheres σ 1/σ 2 is (A)  R1/R2  (B)  R2/R1  (C)  √(R1/R2)  (D)  R12/R22

Tardigrade Admin · Accepted Answer

(q1/q2)=(C1/C2)=(R1/R2) and (q1/q2)=(4π R12σ 1/4π R22σ 2) (R1/R2)=(4π R12σ 1/4π R22σ 2) ∴ (σ 1/σ 2)=(R2/R1)

Q. Two charged spherical conductors of radii $R_{1}$ and $R_{2}$ are connected by a wire. Then the ratio of surface charge densities of the spheres $σ_{1} / σ_{2}$ is

$R_{1} / R_{2}$

$R_{2} / R_{1}$

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

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

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

$\frac{q _{1}}{q _{2}} = \frac{C _{1}}{C _{2}} = \frac{R _{1}}{R _{2}}$
and $\frac{q _{1}}{q _{2}} = \frac{4 π R _{1}^{2} σ _{1}}{4 π R _{2}^{2} σ _{2}}$
$\frac{R _{1}}{R _{2}} = \frac{4 π R _{1}^{2} σ _{1}}{4 π R _{2}^{2} σ _{2}}$
$∴$ $\frac{σ _{1}}{σ _{2}} = \frac{R _{2}}{R _{1}}$

Q. Two charged spherical conductors of radii R1​ and R2​ are connected by a wire. Then the ratio of surface charge densities of the spheres σ1​/σ2​ is

R1​/R2​

R2​/R1​

(R1​/R2​)​

R12​/R22​

R22​/R12​

q2​q1​​=C2​C1​​=R2​R1​​ and q2​q1​​=4πR22​σ2​4πR12​σ1​​ R2​R1​​=4πR22​σ2​4πR12​σ1​​ ∴ σ2​σ1​​=R1​R2​​