• # question_answer 42) The electric potential at a point in free space due to a charge Q coulomb is $Q\times {{10}^{11}}$volts. The electric field at that point is A) $4\pi {{\varepsilon }_{0}}Q\times {{10}^{22}}\,V/m$B) $12\pi {{\varepsilon }_{0}}Q\times {{10}^{20}}\,V/m$C) $4\pi {{\varepsilon }_{0}}Q\times {{10}^{20}}\,V/m$D) $12\pi {{\varepsilon }_{0}}Q\times {{10}^{22}}\,V/m$

The electric potential due to charge Q is $V=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Q}{r}$ where r is the distance of observation point from the charge. At the same point, electric field is $E=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Q}{r}$ Combining Eqs. (i) and (ii), we have $E=\frac{4\pi {{\varepsilon }_{0}}{{V}^{2}}}{Q}=\frac{4\pi {{\varepsilon }_{0}}\times {{(Q\times {{10}^{11}})}^{2}}}{Q}$ $=4\pi {{\varepsilon }_{0}}Q\times {{10}^{22}}\,V/m$