Question
A thin conducting ring of radius $$R$$ is given a charge $$+ Q.$$ The electric field at the centre $$O$$ of the ring due to the charge on the part $$AKB$$ of the ring is $$E.$$ The electric field at the centre due to the charge on the part $$ACDB$$ of the ring is
A.
$$3E\,\,{\text{along}}\,\,KO$$
B.
$$E\,\,{\text{along}}\,\,OK$$
C.
$$E\,\,{\text{along}}\,\,KO$$
D.
$$3E\,\,{\text{along}}\,\,OK$$
Answer :
$$E\,\,{\text{along}}\,\,OK$$
Solution :
Net electric field at the centre of thin conducting ring is zero.
$$\eqalign{ & {E_{{\text{total}}}} = 0 \cr & {E_{AKB}} + {E_{ACDB}} = 0 \cr & {E_{ACDB}} = - {E_{AKB}} \cr & {E_{ACDB}} = E\,{\text{along}}\,OK \cr} $$
Net electric field at the centre of thin conducting ring is zero.
$$\eqalign{ & {E_{{\text{total}}}} = 0 \cr & {E_{AKB}} + {E_{ACDB}} = 0 \cr & {E_{ACDB}} = - {E_{AKB}} \cr & {E_{ACDB}} = E\,{\text{along}}\,OK \cr} $$
