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:[JEE ONLINE 09-04-2013]

[a]                [b]

[c]               [d]

A)             A

B) C

C)             B

D) D

Correct Answer: A

Solution :

[a]

\[e=-\frac{d\phi }{dt}=-\frac{d}{dt}\,(\mathbf{B}\cdot \mathbf{A})\]

\[=-A\cos \theta \frac{d}{dt}(B)\]

\[=-A\,\cos \,\frac{d}{dt}\,\left[ \frac{{{\mu }_{0}}l}{2{{r}_{1}}} \right]\]

\[e=-\frac{A\,\cos \theta {{\mu }_{0}}}{2{{r}_{1}}}\frac{dl}{dt}\]

\[e\propto -\frac{dl}{dt}\]

Means e will vary as the negative of the variation of slope of l(t).