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. ${\mathrm{NBA\omega }}^2$

In a circuit with a coil of resistance \(2~\Omega\), the magnetic flux changes from \(2.0\) Wb to \(10.0\) Wb in \(0.2~\text{s}\). The charge that flows in the coil during this time is:
1. \(5.0~\text{C}\)
2. \(4.0~\text{C}\)
3. \(1.0~\text{C}\)
4. \(0.8~\text{C}\)

A small square loop of wire of side l is placed inside a large square loop of wire of side L (L > l). The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to 

(1) l / L

(2) l² / L

(3) L/l

(4) L²/l

Two coils of self inductance L₁ and L₂ are placed closer to each other so that total flux in one coil is completely linked with other. If M is mutual inductance between them, then 

(1) M = L₁ L₂

(2) M = L₁/L₂

(3) $M=\sqrt{L_1{L}_2}$

(4) M = (L₁ L₂)²