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

1. $\frac{\mathrm{i}∆\mathrm{lsin}\left(\mathrm{\theta }\right)}{{\mathrm{r}}^2}$                               

2. $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{\mathrm{i}∆\mathrm{lsin}\left(\mathrm{\theta }\right)}{\mathrm{r}}$

3. $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{\mathrm{i}∆\mathrm{lsin}\left(\mathrm{\theta }\right)}{{\mathrm{r}}^2}$                         

4. \(\frac{\mu_0}{4 \pi} \mathrm{i} \Delta \mathrm{l} \sin (\theta)\)

To maximise the magnetic field caused by a small element of a current-carrying conductor at a point, the angle between the element and the line connecting the element to the point P must be:

1. 0º

2. 90º

3. 180º

4. 45º

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? (\(\Delta x=1~\mathrm{cm}\))

       
1. \(6\times 10^{-8}~\mathrm{T}\)
2. \(4\times 10^{-8}~\mathrm{T}\)
3. \(5\times 10^{-8}~\mathrm{T}\)
4. \(5.4\times 10^{-8}~\mathrm{T}\)$\mathrm{}$

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?

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

Which one of the following expressions represents Biot-Savart's law? Symbols have their usual meanings.

1. $\stackrel{}{\overrightarrow{dB}}=\frac{{\mu }_0\mathrm{I}(\stackrel{}{\overrightarrow{dl}}\times \hat{r})}{4\mathrm{\pi }{\left|\overrightarrow{\mathrm{r}}\right|}^3}$

2. $\stackrel{}{\overrightarrow{dB}}=\frac{{\mu }_0\mathrm{I}(\stackrel{}{\overrightarrow{dl}}\times \hat{r})}{4\mathrm{\pi }{\left|\overrightarrow{\mathrm{r}}\right|}^2}$

3. $\stackrel{}{\overrightarrow{dB}}=\frac{{\mu }_0\mathrm{I}(\stackrel{}{\overrightarrow{dl}}\times \stackrel{}{\overrightarrow{r}})}{4\mathrm{\pi }{\left|\overrightarrow{\mathrm{r}}\right|}^3}$

4. $\stackrel{}{\overrightarrow{dB}}=\frac{{\mu }_0\mathrm{I}(\stackrel{}{\overrightarrow{dl}}.\stackrel{}{\overrightarrow{r}})}{4\mathrm{\pi }{\left|\overrightarrow{\mathrm{r}}\right|}^3}$

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns. What will the magnetic field be at the centre of this n-turn coil?

1.  nB

2.  n²B

3.  2nB

4.  2n²B

The magnetic induction at point P, which is 4 cm from a long current-carrying wire is 10^-8 Tesla. What would be the field of induction at a distance of 12 cm from the same current?

Two similar coils of radius R are lying concentrically with their planes at right angles to each other. The currents flowing in them are I and 2I, respectively. What will be the resultant magnetic field induction at the centre?

1. $\frac{\sqrt{5}{\mu }_{0}I}{2R}$

2. $\frac{3{\mu }_{0}I}{2R}$

3. $\frac{{\mu }_{0}I}{2R}$

4. $\frac{{\mu }_{0}I}{R}$

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.