Which one of the following gives the value of the magnetic field according to Biot-Savart’s law?

1.	\(\frac{{i} \Delta {l} \sin (\theta)}{{r}^2} \)	2.	\(\frac{\mu_0}{4 \pi} \frac{i \Delta {l} \sin (\theta)}{r} \)
3.	\(\frac{\mu_0}{4 \pi} \frac{{i} \Delta{l} \sin (\theta)}{{r}^2} \)	4.	\(\frac{\mu_0}{4 \pi} {i} \Delta {l} \sin (\theta)\)

A neutral point is obtained at the centre of a vertical circular coil carrying current. The angle between the plane of the coil and the magnetic meridian is :

a) 0                           (b) 45°

(c) 60°                       (d) 90°

A wire carrying current i is shaped as shown. Section AB is a quarter circle of radius r. The magnetic field is directed :

                                                      
(a) At an angle $\mathrm{\pi }/4$ to the plane of the paper

(b) Perpendicular to the plane of the paper and directed in to the paper

(c) Along the bisector of the angle ACB towards AB

(d) Along the bisector of the angle ACB away from AB

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. \(\frac{\mu_{0} I}{4 \pi r}\)
2. \(\frac{\mu_{0} I}{4 \pi r} + \frac{\mu_{0} I}{2 \pi r}\)
3. \(\frac{\mu_{0} I}{4 r} + \frac{\mu_{0} I}{4 \pi r}\)
4. \(\frac{\mu_{0} I}{4 r} - \frac{\mu_{0} I}{4 \pi r}\)

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)?