# Charge Q is distributed to two different metallic spheres having radii R and 2 R such that both spheres have equal surface charge density. Then charge on large sphere is

Q: Charge Q is distributed to two different metallic spheres having radii R and 2 R such that both spheres have equal surface charge density. Then charge on large sphere is

(a) 4Q/5

(b) Q/5

(c) 3Q/5

(d) 5Q/5

Ans: (a)
Sol: If q1 , q2 are the charges on sphere of radii R and 2 R respectively.

Since , σ1 = σ2

$\displaystyle \frac{q_1}{4\pi R^2} = \frac{q_2}{4\pi (2R)^2}$

$\displaystyle q_2 = 4 q_1$

As $q_1 + q_2 = Q$

$5 q_1 = Q$

$q_1 = \frac{Q}{5}$

$q_2 = \frac{4Q}{5}$