Magnetic Flux and Faraday's Law

Q. 5.If R is the electric resistance and C is the capacitance, the dimensional formula of RC is 1) LT^-1 2) T^-1 3) MLT^-2 4) T

Q.

A table with smooth horizontal surface is turning at an angular speed $\omega$ about its axis. A groove is made on the surface along a radius and a particle is gently placed inside the groove at a distance a from the centre. Find the speed of the particle as its distance from the centre becomes L.

1. v = L

2. v =

3. v = a

4. v =

Q. Flux $\varphi$ (in $weber$) in a closed circuit of resistance $10\Omega$ varies with time $t$ (in $seconds$) according to the equation $\varphi =6t^2–5t+1$. What is the magnitude of the induced current at $t=0.25s$?

1. $1.2A$
2. $0.2A$
3. $0.6A$
4. $0.8A$

Q. A conducting loop of radius $R$ is present in an uniform magnetic field $B$ perpendicular to the plane of the ring. If radius $R$ varies as a function of time $‘t^{\prime }$, as $R=R_0+t$. The e.m.f induced in the loop is

1. $2\pi (R_0+t)B$ clockwise
2. $\pi (R_0+t)B$ clockwise
3. $2\pi (R_0+t)B$ anticlockwise
4. Zero

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 positive
4. Both the plates will be negative

Q. An electron and a proton enters into a region of uniform magnetic field at right angles to the field with the same kinetic energy. They describe circular paths of radius $r_e$ and $r_p$ respectively. then-

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

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. 

4. Zero

Q. A flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicular to the plane of the coil. The radius of the coil changes as shown in the figure.

The graph of magnitude of induced emf in the coil is represented by

1. 
2. 
3. 
4. 

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

1. Is zero
2. Decreases as $\frac{1}{r}$
3. Increases as r
4. Decreases as $\frac{1}{r^2}$

Q. A long solenoid has $1000$ turns per meter and its radius is $R=2.5\text{cm}$. Current in the solenoid increases at a rate of $\frac{200}{\pi }\text{A/s}$. Find the magnitude of induced electric field at a point outside the solenoid at a distance $4\text{cm}$ from its axis.

1. $3\times {10}^{-4}\text{V/m}$
2. $6.25\times {10}^{-4}\text{V/m}$
3. $4.5\times {10}^{-4}\text{V/m}$
4. $9.25\times {10}^{-4}\text{V/m}$

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

Q. Which of the following correctly represents the electric field lines for a spherical conductor having a spherical cavity with a charge $Q$ (not at the center) ?

1. 
2. 
3. 
4. 

Q. A long straight wire is parallel to one edge of the loop as shown in the figure. If the current in the long wire varies with time as $I=I_0{e}^{-\frac{t}{\tau }}$, what will be the induced emf in the loop ?

1. $\frac{{\mu }_{0}bI}{\pi \tau }ln\left(\frac{d+a}{d}\right)$
2. $\frac{{\mu }_{0}bI}{2\pi \tau }ln\left(\frac{d+a}{a}\right)$
3. $\frac{2{\mu }_{0}bI}{\pi \tau }ln\left(\frac{d+a}{a}\right)$
4. $\frac{{\mu }_{0}bI}{\pi \tau }ln\left(\frac{d}{d+a}\right)$

Q.

A square loop of side 4 cm is lying on a horizontal table. A uniform magnetic field of 0.5 T is directed downwards at an angle of ${60}^o$ to the vertical as shown in Fig. 25.3. If the field increases from zero to its final value in 0.2 s, the emf induced in the loop will be

1. 1 mV

2. 2 mV

3. 3 mV

4. 4 mV

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

1. Is zero
2. Decreases as $\frac{1}{r}$
3. Increases as r
4. Decreases as $\frac{1}{r^2}$

Q. A coil of square shape $(4m\times 4m)$ is placed in magnetic filed as shown in the figure. Find induced emf in loop.

1. 32 volt
2. 8 volt
3. 16 volt
4. zero

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 square wire loop of $10\text{cm}$ side lies at right angles to a uniform magnetic field of $20\text{T}$ in vertically downwards direction. A $10\text{V}$ light bulb is in a series with the loop as shown in the fig. The magnetic field is decreasing steadily to zero over a time interval $\Delta t$. The bulb will shine with full brightness if $\Delta t$ is equal to

1. $20\text{ms}$
2. $0.02\text{ms}$
3. $2\text{ms}$
4. $0.2\text{ms}$

Q. A loop $ABCDEFA$ of straight edges has six corner points A(0, 0, 0), B(5, 0, 0), C(5, 5, 0), D(0, 5, 0), E(0, 5, 5), F(0, 0, 5). The magnetic field in this region is $\overrightarrow{B}$ = $(3\hat{i}+4\hat{k})T$. The quantity of flux through the loop $ABCDEFA$ (in $Wb$) is

Q. A magnetic field B = 2t T exist in a cylinderical region as shown in figure. A square loop of side l = 2cm is placed inside the cylinder; such that, one of its vertices is at center of the cylinder. EMF induced in side AB of the square is

1. 0.8 mV
2. 0 V
3. 0.2 mV
4. 0.4 mV