Magnetic Flux and Faraday's Law

Q. There is a non-conducting rod of length L and negligible mass with two small balls each of mass m and electric charge Q attached to its ends.the rod can rotate about a fixed vertical axis crossing it distance L/4 from one of its ends. A uniform horizontal electric field E is established. 1.At first the rod is in unstable equilibrium.If it is disturbed slightly in this position, the max velocity attained by the ball which is closer to the axis in subsequent motion is?

Q. Four point charges $-q,+q,+q$ and $-q$ are placed on $y-$ axis at $y=-2d,y=-d,y=+d$ and $y=+2d,$ respectively. The magnitude of the electric field $E$ at a point on the $x-$ axis at $x=D,$ with $D>>d,$ will behave as-

1. $E\propto \frac{1}{D^2}$
2. $E\propto \frac{1}{D^3}$
3. $E\propto \frac{1}{D}$
4. $E\propto \frac{1}{D^4}$

Q.

The relation between the amplitude of electric and magnetic field at any place is given by_.

Q. Using Gauss's law, deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point (i) outside and (ii) inside the shell. Plot a graph showing variation of electric field as a function of r> R and r< R.
(r being the distance from the centre of the shell)

Q. Coil of 800 turns of effective area $0.05m^2$ is kept perpendicular to a magnetic field of magnitude $5\times {10}^{-5}T$. When the plane of the coil is rotated by $90°$around any of its coplanar axis in $0.1s$, the emf induced in the coil will be

1. $2V$
2. $0.2V$
3. $2\times {10}^{-3}V$
4. $0.02V$

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. 
   

Q.

Write SI unit and dimension of the magnetic moment?

Q.

On what factors does the self-inductance of a coil depend?

Q. What are the laws of electromagnetic induction? Explain briefly.

Q. Is magnetic field a conservative field or a non-conservative field? Because the lines of forces formed by it are circular (closed loop) and that is a property of non conservative field. But work done in moving in a closed path is zero, which is a property of conservative field.

Q. An electric dipole of dipole moment p is placed in the position of stable equilibrium in uniform electric field of intensity E. This is rotated through an angle theta from the initial position the potential energy of the electric dipole in the final position is

Q.

What is an example of statically induced EMF?

Q. The distance between charges $5\times {10}^{-11}$C and $-2.7\times {10}^{-11}$C is $0.2m$. The distance at which a third charge should be placed in order that it will not experience any force along the line joining the two charges is

1. 0.65 m
2. 0.556 m
3. 0.350 m
4. 0.44 m

Q. A oil drop of mass m carrying charge-q is to be held stationary in the gravitational field of the earth, what is the magnitude and direction of the electric field?

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. A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be:
(Assume the coil to be short circuited.)

1. Halved
2. Quadrupled
3. Doubled
4. The same

Q.

When a bar magnet falls through a long hollow metal cylinder fixed with its axis vertical, the final acceleration of the magnet is?

1. Equal to $0$

2. Less than $g$

3. Equal to $g$

4. Equal to $g$ in the beginning and then more than $g$

Q.

What is a balance point in potentiometer?

Q. An infinite line charge of uniform electric charge density $\lambda$ lies along the axis electrically conducting infinite cylindrical shell of radius $R.$ At time $t=0,$ the space in the cylinder is filled with a material of permittivity $\epsilon$ and electrical conductivity $\sigma .$ The electrical conduction in the material follows Ohm's law. Which one of the following best describes the subsequent variation of the magnitude of current density $j\left(t\right)$ at any point in the material?

1. 
2. 
3. 
4. 

Q.

A charged particle going around in a circle can be considered to be a current loop. A particle of mass $m$ carrying charge $q$ is moving in a plane with speed $v$ under the influence of magnetic field $B$. The magnetic moment of this moving particle:

1. $\frac{m{v}^{2}B}{2B^2}$

2. $-\frac{m{v}^{2}B}{2\mathrm{\pi }{B}^2}$

3. $-\frac{m{v}^{2}B}{2B^2}$

4. $-\frac{m{v}^{2}B}{B^2}$

Q. What are the important topics in the chapter electromagnetic induction?

Q.

A small circular loop of conducting wire has radius $a$ and carries current$i$. It is placed in a uniform magnetic field$B$ perpendicular to its plane such that when rotated slightly about its diameter and released, its starts performing simple harmonic motion of time period $T$. If the mass of the loop is $m$then

1. $T=\sqrt{\frac{\pi M}{iB}}$

2. $T=\sqrt{\frac{2\pi M}{iB}}$

3. $T=\sqrt{\frac{\pi M}{2iB}}$

4. $T=\sqrt{\frac{2M}{iB}}$

Q.

Consider a circular coil of wire, carrying current $I$, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by ${\phi }_i$ The magnetic flux through the area of the circular coil area is given by ${\phi }_0$.

1. ${\phi }_i=-{\phi }_0$

2. ${\phi }_i>{\phi }_0$

3. ${\phi }_i<{\phi }_0$

4. ${\phi }_i={\phi }_0$

Q.

In a circuit with a coil of resistance $2\Omega$, the magnetic flux changes from $2.0Wb$ to $10.0Wb$ in $0.2s$. The charge that flows in the coil during this time is

1. $5.0C$

2. $4.0C$

3. $1.0C$

4. $0.8C$

Q.

Why is the net force on a current carrying solenoid in uniform magnetic field equal to zero

Q. Give a few applications of Faradays law of induction in daily life.

Q. Electric field and magnetic field of an electromagnetic wave propagating through a medium is given by, $E=E_{\circ }\sin (kx-\omega t)$ and $B=B_{\circ }\sin (kx-\omega t)$ respectively, then -

1. $E_{\circ }k=B_{\circ }\omega$
2. If the electric field is in $y-$direction, then the magnetic field should be in $z-$direction.
3. The speed of the electromagnetic wave is $\frac{E_0}{B_0}$.
4. All the above

Q. Two small balls. Each having charge q, are suspended by two insulating threads of equal length L from a hook in an elevator. The elevator is freely falling. Calculate the angle between the two threads and tension in each thread.

Q.

A conducting circular loop having a radius of 5.0 cm, is placed perpendicular to a magnetic field of 0.50 T. It is removed from the field in 0.50 s. Find the average emf produced in the loop during this time.

Q. A coil of area $100{\text{cm}}^2$ has $500$ turns. Magnetc field of $0.1{\text{weber/m}}^2$ is perpendicular to the plane of coil. The magnetic field is reduced to zero in $0.1\text{s}$. Then induced e.m.f. in the coil is

1. $1\text{V}$
2. $5\text{V}$
3. $50\text{V}$
4. $0\text{V}$