A part of a long wire carrying a current i is bent into a circle of radius r as shown in the figure. The net magnetic field at the centre O of the circular loop is

                         

(1) $\frac{{\mu }_{0}i}{4r}$                                

(2) $\frac{{\mu }_{0}i}{2\mathrm{\pi r}}\left(\mathrm{\pi }+1\right)$

(3) $\frac{{\mu }_{0}i}{2r}$                                

(4) $\frac{{\mu }_{0}i}{2\mathrm{\pi r}}\left(\mathrm{\pi }-1\right)$

What is the magnetic field at point O in the figure?
                    

1.  $\frac{{\mu }_{0}I}{4\mathrm{\pi r}}$                                  
2.  $\frac{{\mu }_{0}I}{4\mathrm{\pi r}}+\frac{{\mu }_{0}I}{2\mathrm{\pi r}}$
3.  $\frac{{\mu }_{0}I}{4r}+\frac{{\mu }_{0}I}{4\mathrm{\pi r}}$                        
4.  $\frac{{\mu }_{0}I}{4r}-\frac{{\mu }_{0}I}{4\mathrm{\pi r}}$

The magnetic moment of a current (i) carrying circular coil of radius (r) and number of turns (n) varies as :

(1) $1/r^2$                            

(2) $1/r$

(3) r                                  

(4) $r^2$

If the current is flowing in the south direction along a power line, then what will be the direction of the magnetic field above the power line (neglecting the earth's field)?

For the magnetic field to be maximum due to a small element of current-carrying conductor at a point, the angle between the element and the line joining the element to the given point must be:

1. 0°                           
2. 90°
3. 180°                        
4. 45°

An electron and a proton enter a magnetic field perpendicularly. Both have the same kinetic energy. Which of the following is true:

1. Trajectory of electron is less curved

2. Trajectory of proton is less curved

3. Both trajectories are equally curved

4. Both move on a straight-line path

A proton, a deuteron, and an $\alpha -$ particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If $r_p,r_d$ and $r_{\alpha }$ denote respectively the radii of the trajectories of these particles, then:

1. $r_{\alpha }=r_p<r_d$                             

2.  $r_a>r_d>r_p$ 

3. $r_{\alpha }=r_d>r_p$                             

4.  $r_p=r_d=r_{\alpha }$ 

An electron and a proton with equal momentum enter perpendicularly into a uniform magnetic field, then :

(1) The path of proton shall be more curved than that of electron

(2) The path of proton shall be less curved than that of electron

(3) Both are equally curved

(4) Path of both will be a straight line

One proton beam enters a magnetic field of ${10}^{-4}T$ normally, Specific charge = ${10}^{11}C/kg.$ velocity = ${10}^{7}m/s.$ What is the radius of the circle described by it:

1. $0.1m$                               

2. $1m$

3. $10m$                               

4. None of these

In a cyclotron, the angular frequency of a charged particle is independent of :

1. Mass                         

2.  Speed

3. Charge                       

4. Magnetic field