A highly conducting ring of radius R is perpendicular to and concentric with the axis of a long solenoid as shown in fig. The ring has a narrow gap of width d in its circumference. The solenoid has a cross-sectional area A and a uniform internal field of magnitude B₀. Now beginning at t = 0, the solenoid current is steadily increased so that the field magnitude at any time t is given by B(t) = B₀ + αt where α > 0. Assuming that no charge can flow across the gap, the end of the ring which has an excess of positive charge and the magnitude of induced e.m.f. in the ring are respectively

(1) X, Aα

(2) X πR²α

(3) Y, πA²α

(4) Y, πR²α

A wire cd of length \(l\) and mass \(m\) is sliding without friction on conducting rails \(ax\) and \(by\) as shown. The vertical rails are connected to each other with a resistance \(R\) between \(a\) and \(b\). A uniform magnetic field \(B\) is applied perpendicular to the plane \(abcd\) such that \(cd\) moves with a constant velocity of:

A conducting rod \(AC\) of length \(4l\) is rotated about point \(O\) in a uniform magnetic field \(\vec {B}\) directed into the paper. If \(AO = l\) and \(OC = 3l\), then:

   
1. \(V_{A} - V_{O} = \dfrac{B \omega l^{2}}{2}\)
2. \(V_{O} - V_{C} = \dfrac{7}{2} B \omega l^{2}\)
3. \(V_{A} - V_{C} = 4 B \omega l^{2}\)
4. \(V_{C} - V_{O} = \dfrac{9}{2} B \omega l^{2}\)

The network shown in the figure is a part of a complete circuit. If at a certain instant the current i is 5 A and is decreasing at the rate of 10³ A/s then V_B – V_A is

(1) 5 V

(2) 10 V

(3) 15 V

(4) 20 V

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:

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 flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicular to the plane of the coil. The radius of the coil changes as shown in the figure. The graph of induced emf in the coil is represented by

(1)

(2)

(3)

(4)