Question

An equilateral triangular loop $ADC$ having some resistance is pulled with a constant velocity $v$ out of a uniform magnetic field directed into the paper (as shown in figure). At time $t=0$, the side $DC$ of the loop is at the edge of the magnetic field.

The induced current $(i)$ versus time $(t)$ graph will be as
A.

B.

C.

D.

Answer 1

Hint: In this question, the details related to the length of the triangular loop, velocity and also the magnetic field is given, using this information in comparison to the induced emf formula, we can predict the relation between current and time, from which the correct graph can be plotted.

Formula used:
$Induced\,Electro\,Motive\,Force\,(EMF)=Blv$

Complete step by step answer:
According to the question, at time $t=0$, the side $DC$ of the loop is at the edge of the magnetic field. So, as the time increases the side $DC$ of the loop is removed from the magnetic field, which means after $t=0$, only the top two edges of the triangular loop remain in the field.
But, since the velocity of the loop is constant, the effective length of the top two edges inside the magnetic field keeps on decreasing with time at constant rate.
Now, from the formula of induced emf, which is:
$Induced\,EMF=Blv$
In the above equation, we can see that:
$B$ is the magnetic field, which is constant.
$v$ is the velocity, which is also constant, and
$l$ is the effective length of the triangular loop, which is decreasing at a constant rate.
So, the emf is also decreasing at a constant rate with time.
And, after the whole loop is outside the magnetic field, no more emf exists in the loop, which means after a certain time there is no emf that exists in the loop, as the triangular loop has exited the magnetic field.
Hence, the correct graph depicting the above scenario is a straight line with constant rate negative slope, which ends at a point in time.
Therefore, the correct answer is Option (B).

Note:
In this type of question, it's better to take all the details given in the question and compare it with the suitable equation, to find the dependency of the quantity and also how this dependency is affecting the final outcome, which will help to predict the graph with proper details.