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Question

# A thin ring of radius R metres is placed in x−y plane such that its centre lies on origin. The half ring in region x<0 carries uniform linear charge density +λ C/m and the remaining half ring in region x>0 carries uniform linear charge density −λ C/m. Then the electric potential (in volts) at point P whose coordinates are (0 m,+R/2 m) is

A
14πϵ0λ2
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B
Zero
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C
14πϵ0λ4
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D
Cannot be determined
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Solution

## The correct option is B ZeroConsider two infinitesimally small elements on ring having charges +dq and −dq symmetrically located about y−axis as shown in figure. Potential due to this pair at any point on y− axis is zero. The sum of potentials due to all such possible pairs is zero at all points on y− axis. Hence potential at P(0,R2) is zero. Hence, option (b) is correct answer.

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