Multiple choice

A semi-circular arc of radius r is charged uniformly and the charge per unit length is λ. The electric field at its centre is

  1. λ/2πє0r2

  2. λ/4πє0r2

  3. λ/3πє0r

  4. λ/2π є0r

  5. λ/21π є0r
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Electric intensity at centre O, due to small element dl of the charged ring dE = λ dl / 4πє0r2 = λ(a dӨ) / 4πє0r2.  As is clear from figure, horizontal components of dE will cancel out in pairs and vertical components will add. π π ... E = ∫dE sinӨ = ∫ λ / 4πє0r (sinӨ dӨ) 0 0 π = λ / 4πє0r [ - cos Ө] o dl dE E = λ / 4πє0r ( - cosπ + cos0) = λ / 2π є0r.

Keep practicing — related questions