Two long straight wires are set parallel to each other. Each carries a current i in the same direction and the separation between them is 2r. The intensity of the magnetic field midway between them is- 

     

(1) ${\mu }_{0}i/r$                            
(2) Zero
(3) $4{\mu }_{0}i/r$                             
(4) ${\mu }_{0}i/4r$

The ratio of the magnetic field at the centre of a current-carrying coil of the radius 'a' and at a distance ‘a’ from centre of the coil along the axis of the coil is:

1. $\frac{1}{\sqrt{2}}$                              2. $\sqrt{2}$ 

3. $\frac{1}{2\sqrt{2}}$                             4. $2\sqrt{2}$ 

The earth’s magnetic field at a given point is $0.5\times {10}^{-5}Wb-m^{-2}.$ This field is to be annulled by magnetic induction at the center of a circular conducting loop of radius 5.0cm. The current required to be flown in the loop is nearly :

(1) 0.2 A                  

(2) 0.4A

(3) 4A                      

(4) 40A

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.  $r_p=r_d=r_{\alpha }$