Home › Previous year questions › GATE 2017 EC (EC2) › Question 34GATE 2017 EC (EC2) – Question 34 Electromagnetics · Maxwell's Equations · 1 mark · Multiple choice
Two conducting spheres S1 and S2, of radii a and b with b>a, are far apart and connected by a long thin conducting wire as shown. For some charge placed on the structure, their potentials are $V_a,V_b$ and surface electric fields are $E_a,E_b$, respectively. Which statement is correct?
$V_a=V_b$ and $E_a<E_b$ $V_a>V_b$ and $E_a>E_b$ $V_a=V_b$ and $E_a>E_b$ $V_a>V_b$ and $E_a=E_b$ Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (C) $V_a=V_b$ and $E_a>E_b$
Explanation Connected conductors in electrostatic equilibrium have equal potentials; otherwise charge would continue moving through the wire. Thus $V_a=V_b=V$.
For a well-separated conducting sphere, $V=Q/(4\pi\epsilon r)$ and the surface-field magnitude is $Q/(4\pi\epsilon r^2)=|V|/r$.
The smaller sphere therefore has the larger surface-field magnitude: $E_a/E_b=b/a>1$. The intended answer is **C**.
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