A square loop of side $2 \mathrm{~cm}$ enters a magnetic field with a constant speed of $2 \mathrm{~cm}…
A square loop of side $2 \mathrm{~cm}$ enters a magnetic field with a constant speed of $2 \mathrm{~cm} \mathrm{~s}^{-1}$ as shown. The front edge enters the field at $t=0 \mathrm{~s}$. Which of the following graph correctly depicts the induced emf in the loop?
(Take clockwise direction positive)
Solution
As the loop moves, there are three cases.
(i) When the loop moves fully outside the magnetic field, there is no change in flux.
$\therefore \varepsilon=\frac{d \phi}{d t}=0$
(ii) When the loop is entering/leaving the area of magnetic field.
$\begin{gathered}\varepsilon=B L V=(0.9)\left(2 \times 10^{-2}\right)\left(2 \times 10^{-2}\right) \\ =2 \times 10^{-4} \mathrm{~V}\end{gathered}$
As flux is in opposite direction to magnetic field.
$\varepsilon$ when loop enters the field $=-2 \times 10^{-4} \mathrm{~V}$
$\varepsilon$ when loop enters the field $=2 \times 10^{-4} \mathrm{~V}$
(iii) When moving inside the magnetic field.
$\frac{d \phi}{d t}=0$
$\therefore$ No emf is induced.
