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Column – I Column – II
A)

Two identical dipoles placed on x-axis at same distance from origin O
P) Electric potential at all points on z-axis is zero
B)

Uniformly charged hemispherical shells; charge density of magnitude $σ,$ signs are as shown
Q) Electric field at any point with $z > 0$ is directed along +z-axis
C)

Uniformly charged semicircular rings, charge density of magnitude $λ$ signs are as shown
R) Electric field at origin is zero.
S) Electric field at any point with $z < 0$ is directed along negative z-axis

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A – R, B – P, C – Q

A – R, B – P, C – S

A – R, B – Q, C – P

A – R, B – S, C – P

answer is C.

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Detailed Solution

Potential $r_{1} < r_{2}$

$V_{+} = \frac{2 k q}{r_{1}} V_{-} = \frac{- 2 k q}{r_{2}} V_{n e t} = V_{+} + V_{-} = 2 k q (\frac{1}{r_{1}} - \frac{1}{r_{2}}) \neq 0$

Electric field :

$E = \frac{k q}{r_{1}^{2}} E' = \frac{k q}{r_{2}^{2}}$

$E' < E,$ hence electric field for z > 0 is directed along +ve z-axis.
$∴$ Similarly for z < 0, electric field is directed along –ve z-axis.
Hence electric field at origin is zero.
Question Image

B) $E_{1} > E_{2},$ hence net electric field is directed along +z-axis.
C) Because equal and opposite charges are distributed on the ring hence potential on z-axis is zero

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