A conducting loop L of surface area S is moving with a velocity $$\overrightarrow {\bf{v}} $$ in a magnetic field $$\overrightarrow {\bf{B}} \left( {\overrightarrow {\bf{r}} ,\,t} \right) = {B_0}{t^2},\,{B_0}$$     is a positive constant of suitable dimensions. The emf induced V_emf in the loop is given by

A. $$ - \int\limits_S {\frac{{\partial \overrightarrow {\bf{B}} }}{{\partial t}}.d\overrightarrow {\bf{S}} } $$

B. $$\oint\limits_L {\left( {\overrightarrow {\bf{v}} \times \overrightarrow {\bf{B}} } \right).d\overrightarrow {\bf{L}} } $$

C. $$ - \int\limits_S {\frac{{\partial \overrightarrow {\bf{B}} }}{{\partial t}}.d\overrightarrow {\bf{S}} } - \oint\limits_L {\left( {\overrightarrow {\bf{v}} \times \overrightarrow {\bf{B}} } \right).d\overrightarrow {\bf{L}} } $$

D. $$ - \int\limits_S {\frac{{\partial \overrightarrow {\bf{B}} }}{{\partial t}}.d\overrightarrow {\bf{S}} } + \oint\limits_L {\left( {\overrightarrow {\bf{v}} \times \overrightarrow {\bf{B}} } \right).d\overrightarrow {\bf{L}} } $$

Answer: Option D