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A non-conducting ring of radius 0 . 5 m carries the total charge of 1.11 × 10 - 10 C , distributed non-uniformly on its circumference, producing an electric field everywhere in space. The value of the line integral ∫ l = ∞ l = 0 - E . d l ( l = 0 being centre of the ring) in volt is

Options

  1. A+ 2
  2. B- 1
  3. C- 2
  4. DZero

Correct answer

A. + 2

Step-by-step solution

By definition, ∫ l = ∞ l = 0 - E → . d l → = V , the potential at the centre of the ring. V = 1 4 π ε 0 . Q R = 9 × 10 9 × 1.11 × 10 - 10 0.5 = 2   V Hence, the value of the given line integral is 2   V

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