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An iron rod of length L and magnetic moment M is bent in the form of a semicircle. Now its magnetic moment will be 
1. M
2. $\frac{2\mathrm{M}}{\mathrm{\pi }}$
3. $\frac{\mathrm{M}}{\mathrm{\pi }}$
4. $\mathrm{M\pi }$

A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It 
1. Will become rigid showing no experiment
2. Will stay in any position 
3. Will stay in north-south direction only
4. Will stay in east-west direction only

The figure shows the various positions (labelled by subscripts ) of small magnetised needles P and Q. The arrows show the direction of their magnetic moment. Which configuration corresponds to the lowest potential energy among all the configurations shown

1. ${\mathrm{PQ}}_3$
2. ${\mathrm{PQ}}_4$
3. ${\mathrm{PQ}}_5$
4. ${\mathrm{PQ}}_6$

A current carrying coil is placed with its axis perpendicular to N-S direction. Let horizontal component of earth's magnetic field be ${\mathrm{H}}_{\mathrm{o}}$ and magnetic field inside the loop be H. If a magnet is suspended inside the loop, it makes angle $\mathrm{\theta }$ with H. Then $\mathrm{\theta }$=
1. ${\tan }^{-1}\left(\frac{H_o}{H}\right)$
2. ${\tan }^{-1}\left(\frac{H}{H_{\mathit{o}}}\right)$
3. $\cos e{c}^{-1}\left(\frac{H}{H_{\mathit{o}}}\right)$
4. $co{t}^{-1}\left(\frac{H_o}{H}\right)$

Two identical bar magnets are placed one above the other such that they are mutually perpendicular and bisect each other. The time period of this combination in a horizontal magnetic field is T. The time period of each magnet in the same field is 
1. $\sqrt{2}T$
2. $2^{\frac{1}{4}}\mathrm{T}$
3. $2^{-\frac{1}{4}}\mathrm{T}$
4. $2^{-\frac{1}{2}}\mathrm{T}$

A thin rectangular magnet suspended freely has a period of oscillation equal to T. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is T' , then ratio T'/T is 
1. $\frac{1}{4}$
2. $\frac{1}{2\sqrt{2}}$
3. $\frac{1}{2}$
4. 2

Two tangent galvanometers having coils of the same radius are connected in series. A current flowing in them produces deflections of 60$°$ and 45$°$ respectively. The ratio of the number of turns in the coils is 
1. 4/3
2. $\left(\sqrt{3}+1\right)/1$
3. $\left(\sqrt{3}+1\right)/\left(\sqrt{3}-1\right)$
4. $\sqrt{3}/1$

Core of electromagnets are made of ferromagnetic material which has 
1. High permeability and high retentivity
2. Low permeability and low retentivity
3. High permeability and low retentivity
4. Low permeability and high retentivity

If a bar magnet of length l and cross-sectional area A is cut into two equal parts as shown in figure, then the pole strength of each pole becomes 

1. half 
2. double 
3. one fourth
4. four times

Two identical short bar magnets, each having magnetic moment M, are placed a distance of 2d apart axes perpendicular to each in a horizontal plane. The magnetic induction at a point midway between them is 
1. $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\left(\sqrt{2}\right)\frac{M}{d^3}$
2. $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\left(\sqrt{3}\right)\frac{M}{d^3}$
3. $\left(\frac{2{\mathrm{\mu }}_0}{\mathrm{\pi }}\right)\frac{M}{d^3}$
4. $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\left(\sqrt{5}\right)\frac{M}{d^3}$

A dip circle is adjusted so that its needle moves freely in the magnetic meridian. In this position, the angle of dip is 40$°$. Now the dip circle is rotated so that the plane in which the needle moves makes an angle of 30$°$ with the magnetic meridian. In this position the needle will dip by an angle
1. 40$°$
2. 30$°$
3. More than 40$°$
4. Less than 40$°$

The true value of angle of dip at a place is 60$°$, the apparent dip in a plane inclined at an angle of 30$°$ with magnetic meridian is 
1. ${\tan }^{-1}\left(\frac{1}{2}\right)$
2. ${\tan }^{-1}\left(2\right)$
3. ${\tan }^{-1}\left(\frac{2}{3}\right)$
4. none of these

The variation of magnetic susceptibility $\left(\mathrm{{\rm X}}\right)$ with absolute temperature T for a ferromagnetic material is 
1. 
2. 
3. 
4. 

The figure illustrates how B, the flux density inside a sample of unmagnetised ferromagnetic material, varies with ${\mathrm{B}}_0$. the magnetic flux density in which the sample is kept. For the sample to be suitable for making a permanent magnet

1. OQ should be large, OR should be small
2. OQ and OR should both be large
3. OQ should be small and OR should be large
4. OQ and OR should both be small

A magnet of length 14 cm and magnetic moment M is broken into two parts of lengths 6 cm and 8 cm. They are put at right angle to each other with opposite poles together. The magnetic moment of the combination is 
1. M/10
2. M
3. M/1.4
4. 2.8 M

A current carrying loop is placed in a uniform magnetic field in four different orientations I,II,III and IV, arrange them in the decreasing order of potential energy 

1. I>III>II>IV
2. I>II>III>IV
3. I>IV>II>III
4. III>IV>I>II

A wire of length L metre carrying current i ampere is bent in the form of a circle. What is the magnitude of magnetic dipole moment ?
1. ${\mathrm{iL}}^2/4\mathrm{\pi }$
2. ${\mathrm{i}}^2{\mathrm{L}}^2/4\mathrm{\pi }$
3. ${\mathrm{i}}^2\mathrm{L}/8\mathrm{\pi }$
4. ${\mathrm{iL}}^2/8\mathrm{\pi }$

The magnetic susceptibility of a paramagnetic substance at -73$°$C is 0.0060, then its value of -173$°$C will be
1. 0.0030
2. 0.0120
3. 0.0180
4. 0.0045 

If the B-H curves of two samples of P and Q of iron are as shown below, then which one of the following statements is correct ?

1. Both P and Q are suitable for making permanent magnet
2. P is suitable for making permanent magnet and Q for making electromagnet
3. P is suitable for making electromagnet and Q is suitable for permanent magnet
4. Both P and Q are suitable for making electromagnets