JEE Main & Advanced
JEE Main Online Paper (Held on 9 April 2013)
question_answer
Two coils, X and Y, are kept in close vicinity of each other. When a varying current, I(t),flows through coil X the induced emf (V (t)) in coil Y, varies in the manner shown here. The variation of I(t), with time, can then be represented by the represented by the graph labeled as graph:
A
B
C
D
JEE Main Online Paper (Held On 09 April 2013)
A)A
B)C
C)B
D)D
Correct Answer:
C
Solution :
\[e=-\frac{d\phi }{dt}=-\frac{d}{dt}\,(\mathbf{B}\cdot \mathbf{A})\] \[=-A\cos \theta \frac{d}{dt}(B)\] \[=-A\,\cos \,\frac{d}{dt}\,\left[ \frac{{{\mu }_{0}}l}{2{{r}_{1}}} \right]\] \[e=-\frac{A\,\cos \theta {{\mu }_{0}}}{2{{r}_{1}}}\frac{dl}{dt}\] \[e\propto -\frac{dl}{dt}\] Means e will vary as the negative of the variation of slope of l(t).