Consider two conducting spheres of radii R1 and R2 with R1 > R2.

Question:

Consider two conducting spheres of radii R1 and R2 with R1 > R2. If the two are at the same potential, the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one.

Solution:

There are two spheres

$\frac{1}{4 \pi \epsilon_{0}} \frac{q_{1}}{R_{1}}$

$\frac{1}{4 \pi \epsilon_{0}} \frac{q_{2}}{R_{2}}$

σ1R1 = σ2R2

σ1/ σ2 = R2/R1

As R2 > R1, that means σ1 > σ2

Therefore, the charge density of the smaller sphere is more than that of the larger sphere.

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