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What is the electric field at the center of a uniformly charged semicircular arc i.e., at point P in Fig.


  • a)

  • b)

  • c)

  • d)

Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the electric field at the center of a uniformly charged semici...


Let λ is the charge per unit length of arc of radius ‘a' splitting the arc in to small segment Δs1  and point charge on each is λΔs1,. From coulomb’s law, the electric field due to the Δs1  is

...(i)

From fig. it is clear that at point PEx will be zero because i E, will be canceled by the contribution from a symmetrically placed Δt on the left half of the arc. So in order to find total E we need only compute Ey at point P. so.

...(ii)

-ve sign arises Because ΔEv is in - y direction sum over the whole are

...(iii)

Along the circle of radius a. ds = adθ

So. 

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Most Upvoted Answer
What is the electric field at the center of a uniformly charged semici...

Let λ is the charge per unit length of arc of radius ‘a' splitting the arc in to small segment Δs1  and point charge on each is λΔs1,. From coulomb’s law, the electric field due to the Δs1  is
...(i)
From fig. it is clear that at point PEx will be zero because i E, will be canceled by the contribution from a symmetrically placed Δt on the left half of the arc. So in order to find total E we need only compute Ey at point P. so.
...(ii)
-ve sign arises Because ΔEv is in - y direction sum over the whole are
...(iii)
Along the circle of radius a. ds = adθ
So. 
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What is the electric field at the center of a uniformly charged semicircular arc i.e., at point P in Fig.a)b)c)d)Correct answer is option 'A'. Can you explain this answer?
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