A) 5 J
B) 6 J
C) 7.5 J
D) 9 J
Correct Answer: C
Solution :
(c) 7.5 J \[\left| \varepsilon \right|=L\frac{\Delta l}{\Delta t}\] \[L=\frac{\left| \varepsilon \right|\Delta t}{\Delta l}+\frac{10\times 0.1}{(10-5)}=0.2\,H\] The magnetic field energies for currents \[{{l}_{1}}\] and \[{{l}_{2}}\] are \[{{U}_{1}}=\frac{1}{2}Ll_{1}^{2}\] and \[{{U}_{2}}=\frac{1}{2}Ll_{2}^{2}\] Change in energy, \[\Delta U={{U}_{2}}-{{U}_{1}}\] \[=\frac{1}{2}Ll_{2}^{2}-\frac{1}{2}Ll_{1}^{2}=\frac{L}{2}(l_{2}^{2}-l_{1}^{2})\] \[=\frac{0.2}{2}({{10}^{2}}-{{5}^{2}})=7.5\,J\]
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