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Question

# Match the following.Column - I Column - II a) Electric field outside a conducting charged sphere e) Constant b)Electric potential outside a conducting charged sphere f) directly proportional to distance from centrec) Electric field inside a non-conducting charged sphereg) inversely proportional to distance from centerd) Electric potential inside a charged conducting sphereh) inversely proportional to the square of distance from center

A
a - h, b - g, c - e, d - f
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B
a - e, b - f, c - h, d - g
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C
a - h, b - g, c - f, d - e
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D
a - g, b - h, c - f, d - e
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Solution

## The correct option is C a - h, b - g, c - f, d - e a ) Electric field outside sphere, take a spherical gaussion surface E×4πr2=Vξ0 E=V4πξ0r2 ∴E ∝1r2 b ) Now E=KVr2 we know V=−∫rdEdr=−KV[1r]r=KVr c ) Apply Gauss law taking a sphere at a distance r we get E×4πr2=43πr3pξ0 E=Pr2ξ ∴E∝r d ) Shell Theorem : electric potential inside a changed conducting sphere is constant and is equal to the value at the surface ∴V=constant

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