A galvanometer of \(50~\Omega \) resistance has 25 divisions. A current of 4 × 10^–4 A gives a deflection of one division. To convert this galvanometer into a voltmeter having a range of 25 V, it should be connected with a resistance of:

1. 2500 Ω as a shunt

2. 2450 Ω as a shunt

3. 2550 Ω in series

4. 2450 Ω in series

The electric charge in uniform motion produces :

(1) An electric field only

(2) A magnetic field only

(3) Both electric and magnetic field

(4) Neither electric nor magnetic field

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. $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{2i}{r}(\mathrm{\pi }+1)$
2. $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{2i}{r}(\mathrm{\pi }-1)$
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

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 straight horizontal parallel wires carry the same current in the same direction, and d is the distance between them. You are given a small magnetic needle that is freely suspended. Which of the following positions will have the needle's orientation independent of the magnitude of the current in the wires?

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. \( B =\frac{\mu_0}{4 \pi} \frac{2 i}{r} \)
2. \(B =\frac{\mu_0}{4 \pi} \frac{r}{2 i} \)
3. \(B =\frac{4 \pi}{\mu_0} \frac{2 i}{r} \)
4. \(B =\frac{4 \pi}{\mu_0} \frac{r}{2 i}\)

The magnetic induction at the centre O in the figure shown is:                                                   

 1. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}\left(\frac{1}{{\mathrm{R}}_1}-\frac{1}{{\mathrm{R}}_2}\right)$                                   2. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}\left(\frac{1}{{\mathrm{R}}_1}+\frac{1}{{\mathrm{R}}_2}\right)$                                                         

 3. $\frac{{\mathrm{\mu }}_0\mathrm{i} }{4}\left({\mathrm{R}}_1-{}_{}{}^{}\mathrm{R}_2\right)$                                      4. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}\left({\mathrm{R}}_1+{\mathrm{R}}_2\right)$