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Question

# Match the following: Column-I Column-II (i). Infinite sheet of charge having positive charges. (a). Uniform non-zero electric field intensity in the vicinity. (ii). At the center of Non-conducting uniformly charged solid sphere. (b). Uniform decreasing potential in the vicinity. (iii). Inside a positively charged conducting sphere taking infinity as a reference point. (c). maximum magnitude of potential.

A
ia,b , iic , iiic
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B
ia,c , iia , iiic
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C
ib,c , iia , iiia
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D
ib,c , iia , iiic
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Solution

## The correct option is A i→a,b , ii→c , iii→cFor an infinite sheet of charge (Lets say in x−y plane), Electric field is given byE=σ2ε0 which does not depend upon the position of unit test charge, therefore electric field is uniform and nonzero as charge on the sheet is nonzero. Since, E=−dVdz ⇒dV=−Edz Thus, Potential decreases uniformly along the direction of electric field. For a uniformly charged non conducting solid sphere, Potential at any inside point is given by Vin=Q8πε0R3(3R2−r2)At center (r=0) ∴Vin=3Q8πε0R Which is the maximum value as Vcenter=32×Vsurface For a charged conducting sphere, assuming potential is zero at infinity. Potential at surface of the sphere is given by Vin=Q4πε0R Thus, we can say that, value of the potential is maximum at every point inside the conducting sphere. Hence, option (a) is the correct answer.

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