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A non conducting ring of radius R(1) is ...

A non conducting ring of radius `R_(1)` is charged such that the linear charge density is `lambda_(1)cos^(2)theta` where `theta` is the polar angle. If the radius is increased to `R_(2)` keeping the charge constant, the linear charge density is changed to `lambda_(2)cos^(2)theta`. The relation connecting `R_(1)`, `R_(2)lambda_(1)` and `lambda_(2)` will be

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