Question

A long solenoid S has n turns per metre, with diameter a. At the centre of this coil, we place a smaller coil of N turns and diameter b (b < a). If the current in the solenoid increases linearly with time, then the emf will be induced in the smaller coil. Which of the following is the correct graph showing |$\varepsilon$ | verses t if current varies as a function of mt2 + C ?

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

Answer 2

As per the data given in the question magnetic field due to current in solenoid S, $B = \mu_{0}nI$

Magnetic flux linked with the smaller coil due to this field is

$\varphi =$NBA, where, a = area of smaller coil $= \pi b^{2}$

$\therefore$ emf induced in the smaller coil,

$\varepsilon = - \frac{d\varphi}{dt} = - \frac{d}{dt}(NB\pi b^{2})$

$= - N\pi b^{2}\frac{dI}{dt}(\mu_{0}n) = - N\pi b^{2}\mu_{0}\frac{dI}{dt}$

As current I varies as a function of $(mt^{2} + C)$

$\therefore\varepsilon = - Nn\mu_{0}\pi b^{2}\frac{d}{dt}(mt^{2} + C)$

$= - Nn\pi\mu_{0}b^{2}(2mt)$

From (i),$|\varepsilon| \propto t$

So correct option is (3)