A milliammeter of 10 mA has a coil resistance of 1 Ω. To use it as an ammeter of range 1 A, the required shunt must have a resistance of:

1. \(\frac{1}{101}~\Omega \)

2. \(\frac{1}{100}~\Omega \)

3. \(\frac{1}{99}~\Omega \)

4. \(\frac{1}{9}~\Omega \)

Two toroids \(1\) and \(2\) have total no. of turns \(200\) and \(100\) respectively with average radii \(40~\text{cm}\) and \(20~\text{cm}\) respectively. If they carry the same current \(i\), what will be the ratio of the magnetic fields along the two loops?
1. \(1:1\)
2. \(4:1\)
3. \(2:1\)
4. \(1:2\)

Three infinitely-long conductors carrying currents $I_1,$ $I_2$ $and$ $I_3$ lie perpendicular to the plane of the paper as shown below.

If the value of integral $\oint \overrightarrow{\mathrm{B}}.\overrightarrow{\mathrm{dl}}$ for the loops ${\mathrm{C}}_1,$ ${\mathrm{C}}_2$ $\mathrm{and}$ ${\mathrm{C}}_3$ $\mathrm{are}$ $2{\mathrm{\mu }}_0,$ $4{\mathrm{\mu }}_0$ $\mathrm{and}$ ${\mathrm{\mu }}_0$ in the units of N/A, respectively, then:

A ring of radius R carries a linear charge density $\lambda$. It is rotating with angular speed $\omega$ about an axis passing through the centre and perpendicular to the plane. What is the magnetic field at its centre?

1.  $\frac{3{\mu }_0\lambda \omega }{2}$

2.  $\frac{{\mu }_0\lambda \omega }{2}$

3.  $\frac{{\mu }_0\lambda \omega }{\pi }$

4.  ${\mu }_0\lambda \omega$  

The figure depicts a cross-section of a large metal sheet with an electric current flowing along its surface. The current in a dl-width strip is (Kdl), where K is a constant. What is the magnetic field at a point P and at a distance x from the metal strips?
    
1.  $\frac{1}{2}{\mu }_{0}Kx$

2.  ${\mu }_{0}K$

3.  $\frac{1}{2}{\mu }_{0}K$

4.  $\frac{{\mu }_{0}Kx}{4}$

1. 0.25 amp

2. 0.8 amp

3. 0.2 amp

4. 0.5 amp

The current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. How much is the resistance of the galvanometer?

Perpendicularly, an electron and a proton enter a magnetic field. Both have the same amount of kinetic energy. Which of the following statements is correct?

A particle having a mass of ${10}^{-2}$ $\mathrm{kg}$ $$carries a charge of $5\times {10}^{-8}$ $\mathrm{C}.$ The particle is given an initial horizontal velocity of ${10}^5$ ${\mathrm{ms}}^{-1}$ in the presence of an electric field $\overrightarrow{\mathbf{E}}$ and magnetic field $\overrightarrow{\mathbf{B}}$. How can we keep the particles moving in a horizontal direction?

Which one of the following pairs of statements are possible?
1. a and c 
2. c and d
3. b and c
4. b and d

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