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

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Ans: (a)

Sol: If q

_{1}, q_{2}are the charges on sphere of radii R and 2 R respectively.Since , σ_{1} = σ_{2}

$\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} $