If a loop changes from an irregular shape to a circular shape, then magnetic flux linked with it:

1. Decreases

2. Remains constant

3. First decreases and then increases

4. Increases

A line charge λ per unit length is lodged uniformly onto the rim of a wheel of mass M and radius R. The wheel has light non-conducting spokes and is free to rotate without friction about its axis (as shown in the figure). A uniform magnetic field extends over a circular region within the rim. It is given by,

$\overrightarrow{B}=B_0 \hat{k} \left(r\le a; a<R\right)$
$= 0 \left(otherwise\right)$

What is the angular velocity of the wheel after the field is suddenly switched off?

1. \(-\frac{2 \pi B_0 a^2 \lambda}{M R} \hat{k}\)
2. \(-\frac{\pi B_0 a^2 \lambda}{M R} \hat{k}\)
3. \(-\frac{2 B_0 a^2 \lambda}{M R} \hat{k}\)
4. \(-\frac{2 B_0 a^2 \lambda}{\pi M R} \hat{k}\)

A straight wire carries a current of 50 A and the loop is moved to the right with a constant velocity, v= 10 m/s. the induced emf in the loop at the instant when x = 0.2 m, is:
(Take a = 0.1 m and assume that the loop has a large resistance.)
 

1.\(3.4 \times10^{-5} V\)
2.\(1.7 \times10^{-5} V\)
3.\(1.7 \times10^{-4} V\)
4.\(3.4 \times10^{-4} V\)
 

An air-cored solenoid having a length of 30 cm whose area is $25 c{m}^2,$ and the number of turns is 500 carries a current of 2.5 A. Suddenly the current is turned off and the time taken for it is ${10}^{-3} s.$ What would be the average value of the induced back-emf across the ends of the open switch in the circuit? (Neglect the variation in the magnetic field near the ends of the solenoid.)

1. 5.5 V

2. 4.5 V

3. 6.5 V

4. 4.0 V

Figure shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutually perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod = 15 cm, B = 0.50 T, resistance of the closed-loop containing the rod = 9.0 mΩ. Assume the field to be uniform.

What is the magnitude of the induced emf if we will keep the K open and the rod is moved with the speed of 12 cm/s in the direction shown in the figure?

1. 9.8 mV
2. 4.9 mV
3. 0.9 mV
4. 9.0 mV

Figure shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutually perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod = 15 cm, B = 0.50 T, resistance of the closed-loop containing the rod = 9.0 mΩ. Assume the field to be uniform.

What is the emf induced in the moving rod if the direction of the magnetic field is changed from perpendicular to parallel to the rails?

1. 0
2. 9 mV
3. 0.9 mV
4. None of these

It is desired to measure the magnitude of the field between the poles of a powerful loudspeaker magnet. A small flat search coil of area $2 c{m}^2$ with 25 closely wound turns, is positioned normal to the field direction, and then quickly snatched out of the field region. Equivalently, one can give it a quick 90° turn to bring its plane parallel to the field direction). The total charge flown in the coil (measured by a ballistic galvanometer connected to the coil) is 7.5 mC. The combined resistance of the coil and the galvanometer is 0.50 $\Omega$. The field strength of the magnet is:

1. 0.55 T
2. 0.75 T
3. 0.67 T
4. 0.49 T

What is the dimensional formula of magnetic flux?

1. $[\mathrm{M}$ ${\mathrm{L}}^2$ ${\mathrm{T}}^{-2}$ ${\mathrm{A}}^{-1}]$

2. $[\mathrm{M}$ ${\mathrm{L}}^1$ ${\mathrm{T}}^{-1}$ ${\mathrm{A}}^{-2}]$

3. $[\mathrm{M}$ ${\mathrm{L}}^2$ ${\mathrm{T}}^{-3}$ ${\mathrm{A}}^{-1}]$

4. $[\mathrm{M}$ ${\mathrm{L}}^{-2}$ ${\mathrm{T}}^{-2}$ ${\mathrm{A}}^{-2}]$

A cylindrical magnet is kept along the axis of a circular coil. On rotating the magnet about its axis, the coil will have induced in it:

A bar magnet is made to fall through a long surface copper tube. The speed (v) of the magnet as a function of time (t) is best represented by: