A current-carrying closed loop in the form of a right-angle isosceles triangle ABC is placed in a uniform magnetic field acting along AB. If the magnetic force on the arm BC is F, the force on the arm AC is:

                         

1. $\mathbf{-}\mathbf{F}$                                               2. $\mathbf{F}$

3. $\sqrt{2}\mathbf{F}$                                             4. $-\sqrt{2}\mathbf{F}$

A uniform electric field and a uniform magnetic field are acting in the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron :

1. speed will decrease

2. speed will increase 

3. will turn towards the left of the direction of motion 

4. will turn towards right of direction a motion

A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current $I_{\mathit{1}}$ at a distance d from the conductor as shown in figure. The loop will experience 

(1) a net repulsive force away from the conductor 

(2) a net torque acting upward perpendicular to the horizontal plane

(3) a net torque acting downward normal to the horizontal plane

(4) a net attractive force towards the conductor 

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 conducting circular loop is placed in a uniform magnetic field, \(B=0.025\) T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of \(1\) mm/s. The induced emf when the radius is \(2\) cm, is:
1. \(2\pi\) \(\mu\)V
2. \(\pi \) \(\mu\)V
3. \(\frac{\pi}{2}\) \(\mu\)V
4. \(2\) \(\mu\)V

 Electromagnets are made of soft iron because soft iron has:

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