• # question_answer From a conducting ring of radius R which carries a charge Q (uniformly distributed) along its periphery a small length $d\ell$ is cut off. The electric field at the  center due to the remaining wire is A) $\frac{Qd\ell }{8{{\pi }^{2}}{{\in }_{0}}{{R}^{3}}}$                           B) $\frac{Q}{4\pi {{\in }_{0}}{{R}^{2}}}$ C)  zero                      D)  can't be determined

Here to solve this quations we can use principle of superposition. The given structure can be considered as combination of two as shown in figure. ${{\vec{E}}_{at}}$ (due to given structure) $={{\vec{E}}_{atO}}(due\,to\,l)-{{E}_{atO}}(due\,to\,all)$$E=\frac{dq}{4\pi {{\in }_{0}}{{R}^{2}}}$towards dl. $=\frac{Q/2\pi R\times d\ell }{4\pi {{\in }_{0}}{{R}^{2}}}=\frac{Qd\ell }{8{{\pi }^{2}}{{\in }_{0}}{{R}^{3}}}$