A current carrying coil is placed with its axis perpendicular to N-S direction. Let horizontal component of earth's magnetic field be ${\mathrm{H}}_0$ and magnetic field inside the loop be H. If a magnet is suspended inside the loop, it makes angle $\mathrm{\theta }$ with H. Then $\mathrm{\theta \; equal\; to:}$

1. ${\tan }^{-1}\left(\frac{H_0}{H}\right)$

2. ${\tan }^{-1}\left(\frac{H}{H_{\mathit{0}}}\right)$

3. $\cos e{c}^{-1}\left(\frac{H}{H_{\mathit{0}}}\right)$

4. $co{t}^{-1}\left(\frac{H_0}{H}\right)$

The vertical component of the earth's magnetic field is zero at:

1. The magnetic poles.

2. The magnetic equator.

3. The geographic poles.

4. The geographic equator.

Select the incorrect statement regarding magnetic material.

The relation amongst the three elements of Earth's magnetic field, namely horizontal component H, vertical component V and dip angle$$ $\delta$ is: ($B_E$=total magnetic field):

1. V=$B_E$tan$\delta$, H=$B_E$

2. V=$B_E$sin$\delta$, H=$B_E$cos$\delta$

3. V=$B_E$cos$\delta$, H=$B_E$sin $\delta$

4. V=$B_E$, H=$B_E$tan$\delta$ 

A frog can be levitated in a magnetic field produced by a current in a vertical solenoid placed below the frog. This is possible because the body of the frog behaves as:

A bar magnet has coercivity \(4\times 10^{3}~\text{Am}^{-1}\). It is desired to demagnetize it by inserting it inside a solenoid \(12~\text{cm}\) long and having \(60\) turns. The current that should be sent through the solenoid is:
1. \(2\) A
2. \(4\) A
3. \(6\) A
4. \(8\) A

A uniform magnetic field, parallel to the plane of the paper existed in space initially directed from left to right. When a bar of soft iron is placed in the field parallel to it, the lines of force passing through it will be represented by:

1.		2.
3.		4.

A dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period of vibration is found to be 2 seconds. If the same needle is then allowed to vibrate in the horizontal plane and the time period is again found to be 2 seconds, then the angle of dip is:

1. 0^o

2. 30^o

3. 45^o

4. 90^o

A closely wound solenoid of \(2000\) turns and area of cross-section \(1.5\times10^{-4}\) m² carries a current of \(2.0\) A. It is suspended through its center and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field \(5\times 10^{-2}\) tesla making an angle of \(30^{\circ}\) with the axis of the solenoid. The torque on the solenoid will be:
1. \(3\times 10^{-3}\) Nm 
2. \(1.5\times 10^{-3}\) Nm 
3. \(1.5\times 10^{-2}\) Nm 
4. \(3\times 10^{-2}\) Nm