Q. No.Four small identical bar magnets, each of magnetic dipole moment \(M\), are placed on the vertices of a square of side \(a\) such that the diagonals of the square coincide with the perpendicular bisectors of the respective magnets. The net magnetic field at the centre of the square is:
1. zero
2. \(\dfrac{\mu_{0}}{\sqrt{2 \pi}} \dfrac{M}{a^{3}}\)
3. \(\dfrac{2 \sqrt{2} \mu_{0}}{\pi} \cdot \dfrac{M}{a^{3}}\)
4. \(\dfrac{\mu_{0}}{\pi} \cdot \dfrac{M}{a^{3}}\)
| 1. | \(285~\text{A/m}\) | 2. | \(2600~\text{A/m}\) |
| 3. | \(520~\text{A/m}\) | 4. | \(1200~\text{A/m}\) |
| 1. | do not exist. |
| 2. | are from the N-pole to the S-pole of the magnet. |
| 3. | are from the S-pole to the N-pole of the magnet. |
| 4. | depend upon the area of the cross-section of the bar magnet |
1. \(0.4~\text T\)
2. \(4~\text T\)
3. \(0.4~\text{mT}\)
4. \(4~\text{mT}\)
A bar magnet of length \(l\) and magnetic moment \(p_{m}\) is bent in the form of an arc as shown in the figure below. The new magnetic dipole moment will be:
| 1. | \(p_{m}\) | 2. | \(\dfrac{3}{\pi }p_{m}\) |
| 3. | \(\dfrac{2}{\pi }p_{m}\) | 4. | \(\dfrac{1}{2 }p_{m}\) |
A long magnetic needle of length 2L, magnetic moment M and pole strength m units is broken into two pieces at the middle. The magnetic moment and pole strength of each piece will be
1.
2.
3.
4. M, m
| 1. | \(\dfrac{3 M}{\pi}\) | 2. | \(\dfrac{4M}{\pi}\) |
| 3. | \(\dfrac{ M}{\pi}\) | 4. | \(\dfrac{2 M}{\pi}\) |
| Statement I: | The poles of magnets cannot be separated by breaking into two pieces. |
| Statement II: | The magnetic moment will be reduced to half when a magnet is broken into two equal pieces. |
| 1. | Statement I is correct and Statement II is incorrect. |
| 2. | Statement I is incorrect and Statement II is correct. |
| 3. | Both Statement I and Statement II are correct. |
| 4. | Both Statement I and Statement II are incorrect. |
| Column-I | Column-II | ||
| \(\mathrm{(A)}\) |  Magnetic field of a bar-magnet at an axial point \(P,\) a large distance \(r\) from the centre. |
\(\mathrm{(I)}\) | \(\dfrac{1}{r^2}\) |
| \(\mathrm{(B)}\) |  Magnetic field of a bar magnet, at an equatorial point, a large distance \(r\) from its centre. |
\(\mathrm{(II)}\) | \(\dfrac{1}{r^3}\) |
| \(\mathrm{(C)}\) |  The force of interaction between two short bar-magnets placed a large distance \(r\) apart, with a common axis. |
\(\mathrm{(III)}\) | \(\dfrac{1}{r^4}\) |
| \(\mathrm{(D)}\) |  The torque between two short bar-magnets placed a large distance \(r,\) apart: with mutually perpendicular axes, as shown. |
\(\mathrm{(IV)}\) | \(\dfrac{1}{r^6}\) |
| 1. | \(\mathrm{A\text-II,B\text-II,C\text-IV,D\text-I}\) |
| 2. | \(\mathrm{A\text-II,B\text-II,C\text-III,D\text-II}\) |
| 3. | \(\mathrm{A\text-II,B\text-I,C\text-III,D\text-IV}\) |
| 4. | \(\mathrm{A\text-I,B\text-I,C\text-II,D\text-III}\) |
A horizontal circular loop carries a current that looks clockwise when viewed from above. It is replaced by an equivalent magnetic dipole consisting of a south pole \(S\) and a north pole \(N.\)
| (a) | The line \(SN\) should be along the diameter of the loop. |
| (b) | The line \(SN\) should be perpendicular to the plane of the loop. |
| (c) | The south pole should be below the loop. |
| (d) | The north pole should be below the loop |
Choose the correct option from the given ones:
1. (a) and (b) only
2. (b) and (d) only
3. (c) and (d) only
4. (a) and (d) only
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