Q.
Two charged conducting spheres of radii a and b are connected to each other by a wire. The ratio of electric fields at the surfaces of two spheres is
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Electrostatic Potential and Capacitance
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Solution:
Let q1 and q2 be the charges and C1 and C2 be the capacitance of two spheres
The charge flows from the sphere at higher potential to the other at lower potential, till their potentials becomes equal.
After sharing, the charges on two spheres would be q2q1=C2VC1V…(i)
Also C2C1=ba…(ii)
From (i)q2q1=ba
Ratio of surface charge on the two spheres σ2σ1=4πa2q1⋅q24πb2 =q2q1⋅a2b2=ab(using(ii)) ∴ The ratio of electric fields at the surfaces of two spheres E2E1=σ2σ1=ab