Faraday's Law

Q. Following figures show the arrangement of bar magnetism in different configurations. Each magnet has magnetic dipole moment $\overrightarrow{m}$ . Which configuration has highest net magnetic dipole moment ?

1. 
2. 
3. 
4. 

Q. A uniform electric field of magnitude $E=100\text{N/C}$ exists in the space in $+x-$ direction. Calculate the flux of this field through a plane square of edge $10\text{cm}$ placed in the $y-z$ plane. Take the normal along the positive $x-$ axis to be positive.

1. $1{\text{N-m}}^2/\text{C}$
2. $2{\text{N-m}}^2/\text{C}$
3. $3{\text{N-m}}^2/\text{C}$
4. $4{\text{N-m}}^2/\text{C}$

Q.

A long solenoid of radius 2 cm has 100 turns/cm and carries a current of 5 A. A coil of radius 1 cm having 100 turns and a total resistance of $20\omega$ is placed inside the solenoid coaxially. The coil is connected to a galvanometer. If the current in the solenoid is reversed in direction, find the charge flown through the galvanometer.

Q. A small plane area is rotated in an electric field. The flux of electric field through the area is maximum when

1. Electric field lines are parallel to the surface
2. Electric field lines are perpendicular to the surface
3. Electric field lines are at ${60}^{\circ }$ to the surface
4. Electric field lines are at ${45}^{\circ }$ to the surface.

Q.

An electric dipole is held in a uniform electric field. Show that the net force acting on it is zero. The dipole is aligned parallel to the field. Find the work done in rotating it through the angle of 180 degrees.

Q.

A copper disc of radius 0.1 m rotates about its centre with 10 revolutions per second in a uniform magnetic field of 0.1 Tesla. The emf induced across the radius of the disc is

1. $\frac{\pi }{10}V$
2. $\frac{2\pi }{10}V$
3. $10\pi mV$
4. $20\pi mV$

Q. An electric field $\overrightarrow{E}=4x\hat{i}-(y^2+1)\hat{j}\text{N/C}$ passes through the box shown in figure. The flux of the electric field through surface $ABCD$ and $BCGF$ are marked as ${\varphi }_1$ and ${\varphi }_{11}$ respectively. The difference between (${\varphi }_1-{\varphi }_{11}$) is (in ${\text{NM}}^2/\text{C}$)

Q. If alternating current of 60 Hz frequency is flowing through inductance of L = 1 mH and drop in delta Vl is 0.6 then alternating current:- (1) 1/pi A (2) 5/pi A (3) 50/pi A (4) 20/pi A

Q. The figure shows four charges fixed on the vertex of a square in the horizontal plane. A charged bead is constrained to move along a wire passing through the centre of the square. Mark the correct statement(s).

1. In gravity free space, a positively charged bead cannot be in equilibrium at any position.
   
2. In gravity free space, a negatively charged bead cannot be in equilibrium at any position.
   
3. In the presence of gravity, a negatively charged bead cannot be in equilibrium position above the plane of fixed charges.
   
4. In the presence of gravity, a positively charged particle can be in equilibrium above the plane of the fixed charges.
   

Q. A straight horizontal copper wire has a current $I=28\text{A}$ flowing through it. What is the mimimum magnitude of magnetic field required to suspend the wire in air by balancing the gravitational force acting on it?
Given: the linear density of wire is $46.6\text{g/m}$

1. $1.6\times {10}^{-2}\text{T}$
2. $2.48\times {10}^{-3}\text{T}$
3. $3.2\times {10}^{-2}\text{T}$
4. $4.2\times {10}^{-2}\text{T}$

Q. The cube shown in the figure has sides of length $L=10.0\text{cm}$. The electric field is uniform, has a magnitude $E=4.00\times {10}^{-3}{\text{NC}}^{-1}$ and is parallel to the $xy$ plane at an angle of ${37}^{\circ }$ measured from the $+x$-axis toward the $+y$-axis.
Given $\sin {37}^{\circ }=0.6$, $\cos {37}^{\circ }=0.8$



$\left(i\right)$ The surface(s) that have zero electric flux through them are

​​​​​​​$[$1 Mark$]$

1. $S_1\text{and}{S}_3$
2. $S_5\text{and}{S}_6$
3. $S_2\text{and}{S}_4$
4. $S_1\text{and}{S}_5$

Q. A compass needle oscillates $20$ times per minute at a place where dip is ${45}^{\circ }$ and $30$ times per minute where dip is ${30}^{\circ }$. The ratio of horizontal component of earth's magnetic at second to first place is-

1. $1.23$
2. $1.63$
3. $1.83$
4. $1.51$

Q. The maximum torque that a dipole of dipole moment $2\times {10}^{-9}\text{Cm}$ would experience in a uniform electric field of magnitude $4\text{N/C}$ is

$[$0.77 Mark$]$

1. $28\times {10}^{-10}\text{Nm}$
2. $8\times {10}^{-9}\text{Nm}$
3. $81\times {10}^{-6}\text{Nm}$
4. $2\times {10}^{-4}\text{Nm}$

Q. Two identical small plastic balls are rubbed against a piece of wool such that both of them recevied approximately 2×10^{12}and 2.5×10^{12} electrons respectively.Now both the charged balls are kept at a dis†an ce of 25 cm in air. Calculate the nature and magnitude of the force between both the balls.If charges on the both balls are increased by 10 percent then calculate the change in electrosatic force between two balls.

Q. Two long thin charged rods with charge density λ each are placed parallel to each other at adistance d apart. The force per unit length exertedon one rod by the other will be where k=1/4π Eo

Q. A system consists of two coils $\text{A}$ & $\text{B}$. The coil $\text{A}$ carries a steady current $I$ while the coil $\text{B}$ is suspended nearby as shown. Now if the system is heated to raise the temperature of two coils steadily then

1. The two coils show attraction.
2. The two coils show repulsion.
3. There is no change in the position of two coils.
4. Induction of current is not possible in coil $B$.

Q.
The above configuration shows three identical bulbs, grade them in order of their brightness.

1. $B_3>B_2=B_1$
2. $B_1=B_2>B_3$
3. $B_3>B_1>B_2$
4. $B_2>B_1>B_3$

Q. If we double the radius of a coil keeping the current through it unchanged, then the magnetic field at any point at a large distance from centre becomes approximately

1. Double
2. Three times
3. Four times
4. One - fourth

Q. A square loop lies in $\text{x-y}$ plane as shown. It carries a steady current $I$ and is subjected to a magnetic field given $\overrightarrow{B}=(\frac{B_{0}z}{L}\hat{j}+\frac{B_{0}y}{L}\hat{k})$, where $B_0$ is a positive constant. The force acting on the side $OA$ is

1. $\frac{1}{2}{B}_{0}IL\hat{j}$
   
2. $\frac{1}{2}{B}_{0}IL\hat{i}$
   
3. $B_{0}IL\hat{j}$
   
4. $B_{o}IL\hat{i}$
   

Q. A wire is bent in the form of an equilateral triangle $PQR$ of side $20\text{cm}$ and carries a current of $2.5\text{A}$. It is placed in a magnetic field $B$ of magnitude $2.0\text{T}$ directed perpendicularly to the plane of the loop. Find the forces on the three sides of the triangle (Given an integer).

Q. The figure shows a conducting loop consisting of a half circle of area $A=0.06m^2$ and three straight segments.
The half circle lies in a uniform changing magnetic field $B=4t^2+2t+5$ (SI unit), where t is the time in
seconds.
An ideal battery E = 2 V is connected as shown and the total resistance of the wire is $2\Omega$. The net current in the loop at t = 5 seconds is:

1. 1 A
2. 1.5 A
3. 0.10 A
4. 0.26 A

Q. A uniform bar of length $L$ carries a current $I$ in the direction from point $\text{a}$ to $\text{b}$. The bar is in uniform magnetic field directed normally inwards. Torque acting on the rod due to magnetic field, about point $\text{a}$, is

1. $BIL$
2. $\frac{BIL}{2}$
3. $BI{L}^2$
4. $\frac{BI{L}^2}{2}$

Q. $\text{ABC}$ is a triangular frame made out of a metallic wire. $\text{BD}$ is a median of the triangular frame joining the vertex $\text{B}$ to the side $\text{AC}$, (Also made of the same metallic wire). It is known that $\text{AB}=6\text{cm, BC}=8\text{cm}$ and $\text{AC}=10\text{cm}$. The cross-sectional area of the wire is $1{\text{mm}}^2$ and its resistivity is $24n\Omega \text{m}$. The triangle $\text{ABC}$ lies in a cylindrical region of magnetic field such that the intersection of the surface of the cylinder with the plane containing the frame forms the circumcircle of triangle $\text{ABC}$. The magnetic field in the region varies at the rate of $0.263\text{T/s}$. What is the magnitude of the induced current in $\text{mA}$ in the median $\text{BD}$ of the frame?

1. $5\text{mA}$
2. $10\text{mA}$
3. $15\text{mA}$
4. $20\text{mA}$

Q. The variation in an alternating emf with time is shown below. Calculate the mean value per cycle of the given emf.

1. $\frac{V_0}{2}$
2. $0$
3. $\frac{V_0}{\sqrt{2}}$
4. $\frac{V_0}{\sqrt{3}}$

Q. The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is

1. $\frac{BR}{2}$
2. $2BR$
3. $\frac{BR}{4}$
4. $BR$

Q. A wire carrying current $I$, bent in the form of a quarter circle, is held at rest on a smooth table with two threads as shown. A uniform magnetic field exists in the region directed into the plane, select the correct alternatives.

1. Net force on wire is zero
2. Net magnetic force on wire is $BIR\sqrt{2}$
3. Tension in the threads is $BIR$
4. Tension in the threads is $BIR\sqrt{2}$

Q. The radius of a coil of wire with $N$ turns is $0.22\text{m}$ and $3.5\text{A}$ current flows clockwise as shown in figure. A long straight wire is carrying a current $54\text{A}$ towards the left as shown. The shortest distance between the straight wire and the coil is $0.05\text{m}$. The magnetic field at the centre of coil is zero. The number of turns $N$ in the coil is:

1. $4$
2. $6$
3. $7$
4. $8$

Q.

A conducting square loop having edges of length 2.0 cm is rotated through ${180}^{\circ }$ about a diagonal in 0.20 a. A magnetic field B exists in the region which is perpendicular to the loop in its initial position. If the average induced emf during the rotation is 20 mV, find the magnitude of the magnetic field.

Q. A small plane area is rotated in an electric field. The flux of electric field through the area is maximum when

1. Electric field lines are parallel to the surface
2. Electric field lines are perpendicular to the surface
3. Electric field lines are at ${60}^{\circ }$ to the surface
4. Electric field lines are at ${45}^{\circ }$ to the surface.

Q. If phase difference between voltage $\left(E\right)$ and current $\left(i\right)$ is $\frac{\pi }{4}$ and frequency, $f=50\text{Hz}$. Calculate the time difference.

1. $1.5\text{ms}$
2. $2.5\text{ms}$
3. $3.5\text{ms}$
4. $4.5\text{ms}$