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

A wooden stick of length $3\mathcal{l}$ is rotated about an end with constant angular velocity $\mathrm{\omega }$ in a uniform magnetic field B perpendicular to the plane of motion. If the upper one third of its length is coated with copper, the potential difference across the whole length of the stick is –

1. $\frac{9\mathrm{B\omega }{\mathcal{l}}^2}{2}$                           

2. $\frac{4\mathrm{B\omega }{\mathcal{l}}^2}{2}$

3. $\frac{5\mathrm{B\omega }{\mathcal{l}}^2}{2}$                           

4. $\frac{\mathrm{B\omega }{\mathcal{l}}^2}{2}$

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 in the form of a circular loop of radius 10 cm lies in a plane normal to a magnetic field of 100 T. If this wire is pulled to take a square shape in the same plane in 0.1 s, average induced emf in the loop is: 

1.  6.70 volt                   

2.  5.80 volt 

3.  6.75 volt                   

4.  5.75 volt