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Two metallic spheres of radii R and 2 R are charged so that both of these have same surface charge density sigma. If they are connected to each other with a conducting wire , in which direction will the charge flow and why ? |
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Answer» Solution :Consider two metallic SPHERES A and B of radius `R_A = R` and `R_B = 2 R` respectively and they have same surface charge density `sigma`. LET `Q_A` and `Q_B` be total charges on spheres A and B and `V_A` and `V_B` be their respective potentials . Then `V_(A) = (Q_(A))/(4pi in_(0) R_A) = (4 pi R^2 sigma)/(4 pi in_(0) R) = (R sigma)/(in_(0))` and `V_(B) = (Q_(B))/(4pi in_(0) R_(B)) = (4pi (2R)^(2)* sigma)/(4 pi in_(0) (2 R)) = (2 R sigma)/(in_(0))`  THUS `V_(B) gt V_(A)` If the two spheres are connected to each other with a conducting wire , then charge will flow from higher potential to lower potential . As `V_(B) gt V_(A)` , hence charge must flow from sphere B to sphere A , TILL they acquire the same potential . |
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