• # question_answer ) A solenoid has 2000 turns wound over a length of 0.30 m. Its area of cross-section is$1.2\,\,\times \,\,{{10}^{-}}^{3}{{m}^{2}}$. Around its central section a coil of 300 turns is wound. If an initial current of 2A in the solenoid is reversed in 0.25 sec, the emf induced in the coil is equal to- A) $6\times {{10}^{-4}}\,Volt$    B) $4.8\times {{10}^{-2}}Volt$C) $6\times {{10}^{-2}}\,Volt$                D) 48 kV

Magnetic field of solenoid, ${{B}_{1}}\,\,=\,\,\frac{{{\mu }_{0}}\,{{N}_{1}}\,{{i}_{1}}}{\ell }$ Magnet flux of coil, ${{\phi }^{2}}\,=\,{{N}_{2}}\,{{B}_{1}}\,{{A}_{2}}\,=\,{{N}_{2}}\,\left( \frac{{{\mu }_{0}}\,{{N}_{1}}\,{{i}_{1}}}{\ell } \right)\,{{A}_{2}}$ $As\,\,{{\phi }^{2}}\,=\,\,M\,{{i}_{1}}\,so\,\,M\,\,=\,\,\frac{{{\phi }_{2}}}{{{i}_{1}}}\,\,=\frac{{{\mu }_{0}}\,{{N}_{1}}\,{{N}_{2\,}}{{A}_{2}}}{\ell }\,$ $\therefore$ induced emf, $\left| e \right|\,\,\,=\,\,\,\frac{{{\mu }_{0}}\,{{N}_{1}}\,{{N}_{2}}\,{{A}_{2}}}{\ell }\,\,\times \,\,\frac{d{{i}_{1}}}{dt}$ $=\,\,\frac{4\pi \times {{10}^{-7}}\times 2000\times 300\times 1.2\times {{10}^{-3}}}{0.30}\,\times \frac{4}{0.25}$ $=\text{ }4.8\,\,\times \,\,{{10}^{-}}^{2}\,Volt$