GATE EC 2017 Set 2 — Question 24
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Electromagnetics → Maxwell's Equations
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Question
Two conducting spheres S1 and S2 of radii and () respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure.
For some charge placed on this structure, the potential and surface electric field on S1 are and , and that on S2 are and , respectively. Then, which of the following is CORRECT?
Correct answer
(C) Vₐ = V_b and Eₐ E_b
Solution
When two conducting spheres are connected by a conducting wire, they are at the same potential at electrostatic equilibrium. Therefore, .The potential of a conducting sphere of radius is given by .
The surface electric field is given by .We can relate and as .
Since , we have:Given , it follows that , which implies .Thus, the correct condition is and .
The surface electric field is given by .We can relate and as .
Since , we have:Given , it follows that , which implies .Thus, the correct condition is and .
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