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

An element \(\Delta l=\Delta x \hat{i}\) is placed at the origin and carries a large current of \(I=10\) A (as shown in the figure). What is the magnetic field on the y-axis at a distance of \(0.5\) m?(\(\Delta x=1~\mathrm{cm}\))
       

A straight wire carrying a current of 12 A is bent into a semi-circular arc of radius 2.0 cm as shown in the figure. Considering the magnetic field B at the centre of the arc, what will be the magnetic field due to the straight segments?

$1. 0$
$2. 1.2\times {10}^{-4} T$
$3. 2.1\times {10}^{-4} T$
$4. None of these$

The resistances of three parts of a circular loop are as shown in the figure. What will be the magnetic field at the centre of O 
(current enters at A and leaves at B and C as shown)?

1.  $\frac{{\mathrm{\mu }}_0\mathrm{I}}{6\mathrm{a}}$

2.  $\frac{{\mathrm{\mu }}_0\mathrm{I}}{3\mathrm{a}}$

3.  $\frac{2{\mathrm{\mu }}_0\mathrm{I}}{3\mathrm{a}}$

4.  0

Which of the following graphs correctly represents the variation of magnetic field induction with distance due to a thin wire carrying current?

1.		2.
3.		4.

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.  $\frac{{\mu }_{0}I}{4r}-\frac{{\mu }_{0}I}{4\mathrm{\pi r}}$

Two identical long conducting wires AOB and COD are placed at a right angle to each other, with one above the other such that 'O' is the common point for the two. The wires carry I₁ and I₂ currents, respectively. Point 'P' is lying at a distance 'd' from 'O' along a direction perpendicular to the plane containing the wires. What will be the magnetic field at the point "P"?

1. $\frac{{\mu }_0}{2\mathrm{\pi d}}\left(\frac{I_1}{I_2}\right)$

2. $\frac{{\mu }_0}{2\mathrm{\pi d}}\left(I_1+I_2\right)$

3. $\frac{{\mu }_0}{2\mathrm{\pi d}}\left(I_1^2+I_2^2\right)$

4. $\frac{{\mu }_0}{2\mathrm{\pi d}}{\left(I_1^2+I_2^2\right)}^{1/2}$

If the magnetic field at the centre of the circular coil is B₀, then what is the distance on its axis from the centre of the coil where  \(B_x=\frac{B_0}{8}~?\)
(R= radius of the coil)

A circular coil is in the y-z plane with its centre at the origin. The coil carries a constant current. Assuming the direction of the magnetic field at x = – 25 cm to be positive, which of the following graphs shows the variation of the magnetic field along the x-axis?

1.		2.
3.		4.

A current loop consists of two identical semicircular parts each of radius \(R\), one lying in the x-y plane, and the other in the x-z plane. If the current in the loop is \(i\), what will be the resultant magnetic field due to the two semicircular parts at their common centre?