A rectangular loop carrying a current \(\mathrm{I_1}\), is situated near a long straight wire carrying a steady current \(\mathrm{I_2}\). If the wire is parallel to one of the sides of the loop and is in the plane of the loop as shown in the figure, then the current loop will:
         

1.	move away from the wire.
2.	move towards the wire.
3.	remain stationary.
4.	rotate about an axis parallel to the wire.

When will the current sensitivity of a moving coil galvanometer be high?
(N = number of turns, B = magnetic field, A = area of coil, and C = Torsional constant of spring)

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. \(1:2\)

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:

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.  $\frac{{\mu }_{0}Kx}{4}$

Ionized hydrogen atoms and \(\alpha\text-\)particles with the same momenta enter perpendicular to a constant magnetic field, \(B\). The ratio of their path radii \(r_\text{H}:r_\alpha\) will be:

Two circular coils 1 and 2 are made from the same wire but the radius of the 1^st coil is twice that of the 2^nd coil. What is the ratio of the potential difference applied across them so that the magnetic field at their centres is the same?
1. 3
2. 4
3. 6
4. 2