The self inductance of a coil is L. Keeping the length and area same, the number of turns in the coil is increased to four times. The self inductance of the coil will now be 

(1) $\frac{1}{4}L$

(2) L

(3) 4 L

(4) 16 L

A thin semi-circular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction $\overrightarrow{\mathrm{B}}$ (see figure).

At the position MNQ the speed of the ring is v and the potential difference developed across the ring is

1. zero 

2. ${\mathrm{Bv\pi R}}^2 /2$ and M is at higher potential 

3. $\mathrm{\pi RBv}$ and Q is at higher potential 

4. $2\mathrm{RBv}$ and Q is at higher potential.

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)

A uniform but time-varying magnetic field $\mathrm{B}\left(\mathrm{t}\right)$ exists in a circular region of radius $\mathrm{a}$ and is directed into the plane of the paper, as shown.

The magnitude of the induced electric field at point $\mathrm{P}$ at a distance $\mathrm{r}$ from the centre of the circular region :

1.  is zero                             

2.  decreases as $1/\mathrm{r}$ 

3.  increases as $\mathrm{r}$               

4.  decreases as $1/{\mathrm{r}}^2$

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

(1) $\frac{mgR}{Bl}$

(2) $\frac{mgR}{B^2{l}^2}$

(3) $\frac{mgR}{B^3{l}^3}$

(4) $\frac{mgR}{B^{2}l}$

The network shown in the figure is a part of a complete circuit. If at a certain instant, the current \(i\) is \(5~\text{A}\) and is decreasing at the rate of \(10^3~\text{A/s}\), then \(V_B-V_A\) is:

1. \(5~\text{V}\)
2. \(10~\text{V}\)
3. \(15~\text{V}\)
4. \(20~\text{V}\)

The magnetic flux through a coil varies with time as $\mathrm{\varphi }= 5{\mathrm{t}}^2+6\mathrm{t}+9$. The ratio of emf at t = 3s to t = 0s will be 

1.  1 : 9                           

2.  1 : 6 

3.  6 : 1                           

4.  9 : 1

In the figure magnetic energy stored in the coil is 

(1) Zero

(2) Infinite

(3) 25 joules

(4) None of the above

Two circuits have coefficient of mutual induction of 0.09 henry. Average e.m.f. induced in the secondary by a change of current from 0 to 20 ampere in 0.006 second in the primary will be 

(1) 120 V

(2) 80 V

(3) 200 V

(4) 300 V

A coil having number of turns N and cross-sectional area A is rotated in a uniform magnetic field B with an angular velocity $\mathrm{\omega }$. The maximum value of the emf induced in it is –

1. $\frac{\mathrm{NBA}}{\mathrm{\omega }}$                             

2. $\mathrm{NBA\omega }$

3. $\frac{\mathrm{NBA}}{{\mathrm{\omega }}^2}$                             

4. ${\mathrm{NBA\omega }}^2$