a ring of radius R has a charge Q it is cut by the dl. find the electric field at the centre
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The electric field due to full ring is zero at center when arc of length dl is cut, the electric field becomes non zero, so
E small arc =−E rest of portion
If λ be the line charge density, Q=λ.2πr⇒λ=Q/ 2πr
Charge on cut part is dq=λ.dl= Qdl /2πr
The electric field at center due to arc of length dl is E =1/ 4πϵ *Qdl/2pie r^3
=Qdl /8π^2 ϵ r^2
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