Two metal spheres of radii r1 and r2 are charged to the same potential. The ratio of the charge on the two spheres is

Question

Two metal spheres of radii r1 and r2 are charged to the same potential. The ratio of the charge on the two spheres is (A) 1 (B)  (1/2)  (C)  r1-r2  (D)  r1/r2

Tardigrade Admin · Accepted Answer

We know that the potential for a metal sphere V=k(q/r) According to the question V1=k(q1/r1) and V1=k(q2/r2) as V1=V2 k(q1/r1)=k(q2/r2) (q1/r2)=(r1/r2)

Q. Two metal spheres of radii $r_{1}$ and $r_{2}$ are charged to the same potential. The ratio of the charge on the two spheres is

1

$\frac{1}{2}$

$r_{1} - r_{2}$

$r_{1} / r_{2}$

We know that the potential for a metal sphere
$V = k \frac{q}{r}$
According to the question
$V_{1} = k \frac{q _{1}}{r _{1}}$
and $V_{1} = k \frac{q _{2}}{r _{2}}$
as $V_{1} = V_{2}$
$k \frac{q _{1}}{r _{1}} = k \frac{q _{2}}{r _{2}}$
$\frac{q _{1}}{r _{2}} = \frac{r _{1}}{r _{2}}$

Q. Two metal spheres of radii r1​ and r2​ are charged to the same potential. The ratio of the charge on the two spheres is

1

21​

r1​−r2​

r1​/r2​

We know that the potential for a metal sphere V=krq​ According to the question V1​=kr1​q1​​ and V1​=kr2​q2​​ as V1​=V2​ kr1​q1​​=kr2​q2​​ r2​q1​​=r2​r1​​

Q. Two metal spheres of radii $r_{1}$ and $r_{2}$ are charged to the same potential. The ratio of the charge on the two spheres is

$\frac{1}{2}$

$r_{1} - r_{2}$

$r_{1} / r_{2}$

We know that the potential for a metal sphere
$V = k \frac{q}{r}$
According to the question
$V_{1} = k \frac{q _{1}}{r _{1}}$
and $V_{1} = k \frac{q _{2}}{r _{2}}$
as $V_{1} = V_{2}$
$k \frac{q _{1}}{r _{1}} = k \frac{q _{2}}{r _{2}}$
$\frac{q _{1}}{r _{2}} = \frac{r _{1}}{r _{2}}$