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?

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 :

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

The maximum kinetic energy of the positive ion of charge q and mass m in the cyclotron of radius \(r_o\) in which applied magnetic field is B, is:

1. $\frac{q^{2}B{r}_0}{2m}$                        

2. $\frac{q{B}^2{r}_0}{2m}$

3. $\frac{q^2{B}^2{r}_0^2}{2m}$                        

4. $\frac{qB{r}_0}{2m^2}$