Magnetic Flux and Faraday's Law

Q. The flux linked with a coil any instant t is given by $\varphi =10t^2-50t+250$. instantaneous induced emF at $t=35\text{Sec}$ is

1. $450\text{V}$
2. $650\text{V}$
3. $950\text{V}$
4. $720\text{V}$

Q.
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 cross sectional area A and a uniform internal field of magnitude $B_0$. Now beginning at t = 0, the solenoid current is steadily increased so that the field magnitude at any time t is given by $B\left(t\right)=B_0+\alpha twhere\alpha >0$ . Assuming that no charge can flow across the gap, the end of ring which has excess of positive charge and the magnitude of induced e.m.f. in the ring are respectively

1. $X\pi R^2\alpha$
   
2. $X,A\alpha$
   
3. $Y,\pi A^2\alpha$
   
4. $Y,\pi R^2\alpha$

Q. Shown in the figure is a circular loop of radius r and resistance R. A variable magnetic field of induction $B=B_0{e}^{-t}$ is established inside the coil. If the key (K) is closed, the electrical power developed right after closing the switch is equal to

1. $\frac{B_0^2{\pi }^2{r}^4}{R}$
2. $\frac{B_0^2\pi r^2}{R}$
   
3. $\frac{B_{0}10r^3}{R}$
   
4. $\frac{B_0^2{\pi }^2{r}^{4}R}{5}$
   

Q. Square loop ABCD of area $20c{m}^2$ and resistance $5\Omega$ is rotated in a magnetic field B = 2T through ${180}^{\circ }$, with field perpendicualr to the loop initially. In 0.01 seconds the magnitude of induced e.m.f is …………….

1. 0.4 V
2. 0.8 V
3. 0.6 V
4. 1.0 V

Q. A conducting square loop of each side `I' and resistance R moves in a plane with uniform velocity `v perpendicular to one of its sides. A magnetic induction B, constant in time and space, pointing perpendicular and into the plane of loop exists every where. The current induced in the loop is

1. Zero
2. $B\frac{V}{R}$ clock wise
   
3. $2B\frac{V}{R}$ Anti -clock wise
   
4. $B\frac{V}{R}$ anti clock wise
   

Q. The north and south poles of two identical magnets approach a coil with equal speeds from opposite sides. Then

1. Plate 1 will be negative and plate 2 positive
2. Plate 1 will be positive and plate 2 negative
3. Both the plates will be negative
4. Both the plates will be positive

Q. In the following figure, the magnet is moved towards the coil with a speed v and induced emf is e. If magnet and coil recede away from one another each moving with speed v, the induced emf in the coil will be

1. e
2. 2e
3. 4e
4. e/2

Q. A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region

Q. A circular loop of radius R carrying current I lies in x-y plane with its centre at origin. The total magnetic flux through x-y plane is

1. Zero
2. Directly proportional to I
3. Directly proportional to R
4. Directly proportional to $R^2$

Q.

A conducting square loop of side L and resistance R moves in its plane with a uniform velocity $v$ perpendicular to one of its sides. It is sorrounded by a magnetic field B which is constant in time and space and is pointing perpendicularly into the plane of the loop. The current induced in the loop is

1. 
   

2. 
   

3. Zero

4.