A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle 2θ. The earth’s magnetic field component in the direction perpendicular to swing is B. Maximum potential difference induced across the pendulum is 

1. $2BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^{1/2}$

2. $BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

3. $BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^{3/2}$

4. $BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^2$

The variation of induced emf (E) with time (t) in a coil if a short bar magnet is moved along its axis with a constant velocity is best represented as:
    

1.		2.
3.		4.

A loop abcd is moved across the pole pieces of a magnet as shown in fig. with a constant speed v. When the edge ab of the loop enters the pole pieces at time t = 0 sec. , which one of the following graphs represents correctly the induced emf in the coil?

(1)

(2)

(3)

(4)

Some magnetic flux is changed from a coil of resistance 10 ohm. As a result an induced current is developed in it, which varies with time as shown in figure. The magnitude of change in flux through the coil in webers is

(1) 2

(2) 4

(3) 6

(4) None of these

The graph gives the magnitude B(t) of a uniform magnetic field that exists throughout a conducting loop, perpendicular to the plane of the loop. Rank the five regions of the graph according to the magnitude of the emf induced in the loop, greatest first

(1) b > (d = e) < (a = c)

(2) b > (d = e) > (a = c)

(3) b < d < e < c < a

(4) b > (a = c) > (d = e)

Figure (i) shows a conducting loop being pulled out of a magnetic field with a speed v. Which of the four plots shown in figure (ii) may represent the power delivered by the pulling agent as a function of the speed v

(1) a

(2) b

(3) c

(4) d

A rectangular loop is being pulled at a constant speed v, through a region of certain thickness d, in which a uniform magnetic field B is set up. The graph between position x of the right-hand edge of the loop and the induced emf E will be-

(1)  (2)

(3)  (4)

The current i in an induction coil varies with time t according to the graph shown in figure. Which of the following graphs shows the induced emf (e) in the coil with time

(1)               (2)
(3)                 (4)

Switch \(S\) of the circuit shown in the figure is closed at \(t=0\). If \(e\) denotes the induced emf in \(L\) and \(i\) denotes the current flowing through the circuit at time \(t\), then which of the following graphs is correct?

1.		2.
3.		4.

A square loop of side 5 cm enters a magnetic field with 1 cms^-1. The front edge enters the magnetic field at t = 0 then which graph best depicts emf

(1)

(2)

(3)

(4)