Two metal spheres of radius and have same surface charge density . If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes and , respectiv

Question

Two metal spheres of radius  and  have same surface charge density . If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes  and , respectively. The ratio  is.

Canvas Classes · Accepted Answer

🧠 Touch Two Spheres: Charge Splits by Radius, So σ Goes as 1/r

When two metal spheres touch, they become one single conductor. One conductor has one potential all over it. That single fact runs the whole problem. Equal potential means  is the same for both, so charge shares out in proportion to radius: .

Now the key for THIS question. They ask about surface charge density , not charge. Since  and , we get . So the smaller sphere ends up with the HIGHER density. The starting  being equal is ju

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