Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency f Hz. The magnitude of magnetic induction at the center of the ring is :

(1) $\frac{{\mathrm{\mu }}_0\mathrm{q} f}{2\mathrm{R}}$                                       

(2) $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2f\mathrm{R}}$

(3) $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2\mathrm{\pi }f\mathrm{R}}$                                       

(4) $\frac{{\mathrm{\mu }}_0\mathrm{q} f}{2\mathrm{\pi R}}$

A beam of cathode rays is subjected to crossed Electric (E) and magnetic fields(B). The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by:

1. $\frac{B^2}{2V{E}^2}$                                             

2. $\frac{2V{B}^2}{E^2}$

3. $\frac{2V{E}^2}{B^2}$                                           

4. $\frac{E^2}{2V{B}^2}$

(where V is the potential difference between cathode and anode)

A galvanometer has a coil of resistance $100\Omega$ and gives a full scale deflection for 30 mA current.If it is to work as a voltmeter of 30V range, the resistance required to be added will be 

(1) 900 $\Omega$                                     

(2) 1800 $\Omega$

(3) 500 $\Omega$                                     

(4) 1000 $\Omega$

A square current carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is $\overrightarrow{F}$, the net force on the remaining three arms of the loop is

1. 3$\overrightarrow{F}$                 

2. $-$$\overrightarrow{F}$

3. $-$3$\overrightarrow{F}$               

4.  $\overrightarrow{F}$

A closely wound solenoid of 2000 turns and area of cross-section $1.5\times {10}^{-4} {\mathrm{m}}^2$ carries a current of $2.0 \mathrm{A}.$ It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field $5\times {10}^{-2} \mathrm{T}$ making an angle of $30°$ with the axis of the solenoid. The torque on the solenoid will be

1. $3\times {10}^{-3} \mathrm{N}‐\mathrm{m}$                                 

2. $1.5\times {10}^{-3} \mathrm{N}‐\mathrm{m}$

3. $1.5\times {10}^{-2} \mathrm{N}‐\mathrm{m}$                               

4. $3\times {10}^{-2} \mathrm{N}‐\mathrm{m}$

A particle having a mass of ${10}^{-2} \mathrm{kg}$carries a charge of $5\times {10}^{-8} \mathrm{C}.$ The particle is given an initial horizontal velocity of ${10}^5 {\mathrm{ms}}^{-1}$ in the presence of electric field $\overrightarrow{\mathbf{E}}$ and magnetic field $\overrightarrow{\mathbf{B}}$. To keep the particle moving in a horizontal direction, it is necessary that

(1) $\overrightarrow{\mathbf{B}}$ should be perpendicular to the direction of velocity and $\overrightarrow{\mathbf{E}}$ should be along the direction of velocity.

(2) Both $\overrightarrow{\mathbf{B}}$ and $\overrightarrow{\mathbf{E}}$ should be along the direction of velocity.

(3) Both $\overrightarrow{\mathbf{B}}$ and $\overrightarrow{\mathbf{E}}$ are mutually perpendicular and perpendicular to the direction of velocity.

(4) $\overrightarrow{\mathbf{B}}$ should be along the direction of velocity and $\overrightarrow{\mathbf{E}}$ should be perpendicular to the direction of velocity.

Which one of the following pairs of statements are possible?

1.   (1) and (3)                                       2.    (3) and (4)

3.   (2) and (3)                                       4.   (2) and (4)

Under the influence of a uniform magnetic field, a charged particle moves with constant speed v in a circle of radius R. The time period of rotation of the particle -

1. depends on v and not on R

2. depends on R and not on v

3. is independent of both v and R

4. depends on both v and R

The magnetic force acting on a charged particle of charge $-2\mu C$ in a magnetic field of 2T acting in y-direction, when the particle velocity is $\left(2\hat{i}+3\hat{j}\right)\times {10}^6 m{s}^{-1}$ is.

1. 8 N in -z-direction

2. 4 N in z-direction

3. 8 N in y-direction

4. 4 N in y-direction

A galvanometer having a coil resistance of $60\Omega$ shows full scale deflection when a current of 1.0A passes through it. It can be converted into an ammeter to read currents upto 5.0A by 

1. putting in series resistance of 240$\Omega$

2. putting in parallel resistance of 240$\Omega$

3. putting in series resistance of 15$\Omega$

4. putting in parallel resistance of 15$\Omega$