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.

The magnetic field at center due to the orbital motion of the electron in the hydrogen atom is :

1.  12.5 tesla

2.  5 tesla

3.  24 tesla

4.  1 tesla

A long solenoid has 800 turns per meter length of the solenoid. A current of 1.6 A flows through it. The magnetic induction at the end of the solenoid on its axis is:

1.  $16\times {10}^{-4}<mspace\; width="1em"></mspace>\mathrm{T}$

2.  $8\times {10}^{-4}<mspace\; width="1em"></mspace>\mathrm{T}$

3.  $32\times {10}^{-4}<mspace\; width="1em"></mspace>\mathrm{T}$

4.  $4\times {10}^{-4}<mspace\; width="1em"></mspace>\mathrm{T}$

An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of \(i\) amperes and the radius of the circular loop is \(r\) metres. What will be the magnetic induction at its centre?
                   
1. \(\frac{\mu_{0}}{4 \pi} \frac{2 i}{r} \left( \pi + 1 \right)\)
2. \(\frac{\mu_{0}}{4 \pi} \frac{2 i}{r} \left(\pi - 1 \right)\)
3. zero
4. Infinite

A current \(i\) ampere flows in a circular arc of wire whose radius is \(R,\) which subtend an angle $\raisebox{1ex}{$3\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ radian at its centre. The magnetic induction \(B\) at the centre is:
1. \(\frac{\mu_0i}{R}\)
2. \(\frac{\mu_0i}{2R}\)
3. \(\frac{2\mu_0i}{R}\)
4. \(\frac{3\mu_0i}{8R}\)

A straight section PQ of a circuit lies along the X-axis from x=$\frac{-\mathrm{a}}{2}$ to x= $\frac{\mathrm{a}}{2}$ and carries a steady current i. The magnetic field due to the section PQ at a point X = + a will be:

1. Proportional to a             2. Proportional to $a^2$
3. Proportional to $\frac{1}{a}$           4. Zero

A circular coil of radius R carries an electric current. The magnetic field due to the coil at a point on the axis of the coil located at a distance r from the centre of the coil, such that r >> R, varies as 

1. $\frac{1}{r}$                                          

2. $\frac{1}{r^{3/2}}$

3. $\frac{1}{r^2}$                                          

4. $\frac{1}{r^3}$ 

The magnetic induction due to an infinitely long straight wire carrying a current \(i\) at a distance \(r\) from the wire is given by:
1. \( B =\dfrac{\mu_0}{4 \pi} \dfrac{2 i}{r} \)
2. \(B =\dfrac{\mu_0}{4 \pi} \dfrac{r}{2 i} \)
3. \(B =\dfrac{4 \pi}{\mu_0} \dfrac{2 i}{r} \)
4. \(B =\dfrac{4 \pi}{\mu_0} \dfrac{r}{2 i}\)