Dipole in a Magnetic Field
PHXII05:MAGNETISM and MATTER

360405 A bar magnet of magnetic moment 2\(Am\) free to rotate about a vertical axis pass through its centre. The magnet is released from rest from east - west position. Then the \(K.E\) of the magnet as it takes north - south position is \(\left(B_{l I}=25 \mu T\right)\)

1 \(25\,\mu J\)
2 \(50\,\mu J\)
3 \(100\,\mu J\)
4 \(12.5\,\mu J\)
PHXII05:MAGNETISM and MATTER

360406 With reference to magnetic dipole, match the terms of Column I with the items of Column II and choose the correct option from the codes given below.
Column I
Column II
A
Equatorial field for a short dipole
P
\(\frac{{{\mu _0}}}{{4\pi }}\frac{{2M}}{{{r^3}}}\)
B
Axial field for a short dipole
Q
\( - \overrightarrow M \cdot \vec B\)
C
Torque on a dipole
R
\(\overrightarrow M \times \vec B\)
D
Potential energy of a dipole
S
\(\frac{{{\mu _0}}}{{4\pi }}\frac{M}{{{r^3}}}\)

1 A-R, B-P, C-Q, D-S
2 A-S, B-P, C-R, D-Q
3 A-S, B-Q, C-R, D-P
4 A-Q, B-S, C-P, D-R
PHXII05:MAGNETISM and MATTER

360407 The magnetic moment of a bar magnet is \(0.5\,A{m^2}.\) It is suspended in a uniform magnetic field of \(8 \times {10^{ - 2}}\;T.\) The work done in rotating it from its most stable to most unstable position is

1 \(4 \times {10^{ - 2}}\;J\)
2 \(8 \times {10^{ - 2}}\;J\)
3 \(16 \times {10^{ - 2}}\;J\)
4 zero
PHXII05:MAGNETISM and MATTER

360408 The work done in turning a magnet of magnetic moment \(M\) by an angle of \(90^{\circ}\) from the meridian is \(n\) times the corresponding work done to turn it through an angle of \(60^{\circ}\) :

1 \(n=1 / 2\)
2 \(n=2\)
3 \(n=1 / 4\)
4 \(n=1\)
PHXII05:MAGNETISM and MATTER

360405 A bar magnet of magnetic moment 2\(Am\) free to rotate about a vertical axis pass through its centre. The magnet is released from rest from east - west position. Then the \(K.E\) of the magnet as it takes north - south position is \(\left(B_{l I}=25 \mu T\right)\)

1 \(25\,\mu J\)
2 \(50\,\mu J\)
3 \(100\,\mu J\)
4 \(12.5\,\mu J\)
PHXII05:MAGNETISM and MATTER

360406 With reference to magnetic dipole, match the terms of Column I with the items of Column II and choose the correct option from the codes given below.
Column I
Column II
A
Equatorial field for a short dipole
P
\(\frac{{{\mu _0}}}{{4\pi }}\frac{{2M}}{{{r^3}}}\)
B
Axial field for a short dipole
Q
\( - \overrightarrow M \cdot \vec B\)
C
Torque on a dipole
R
\(\overrightarrow M \times \vec B\)
D
Potential energy of a dipole
S
\(\frac{{{\mu _0}}}{{4\pi }}\frac{M}{{{r^3}}}\)

1 A-R, B-P, C-Q, D-S
2 A-S, B-P, C-R, D-Q
3 A-S, B-Q, C-R, D-P
4 A-Q, B-S, C-P, D-R
PHXII05:MAGNETISM and MATTER

360407 The magnetic moment of a bar magnet is \(0.5\,A{m^2}.\) It is suspended in a uniform magnetic field of \(8 \times {10^{ - 2}}\;T.\) The work done in rotating it from its most stable to most unstable position is

1 \(4 \times {10^{ - 2}}\;J\)
2 \(8 \times {10^{ - 2}}\;J\)
3 \(16 \times {10^{ - 2}}\;J\)
4 zero
PHXII05:MAGNETISM and MATTER

360408 The work done in turning a magnet of magnetic moment \(M\) by an angle of \(90^{\circ}\) from the meridian is \(n\) times the corresponding work done to turn it through an angle of \(60^{\circ}\) :

1 \(n=1 / 2\)
2 \(n=2\)
3 \(n=1 / 4\)
4 \(n=1\)
PHXII05:MAGNETISM and MATTER

360405 A bar magnet of magnetic moment 2\(Am\) free to rotate about a vertical axis pass through its centre. The magnet is released from rest from east - west position. Then the \(K.E\) of the magnet as it takes north - south position is \(\left(B_{l I}=25 \mu T\right)\)

1 \(25\,\mu J\)
2 \(50\,\mu J\)
3 \(100\,\mu J\)
4 \(12.5\,\mu J\)
PHXII05:MAGNETISM and MATTER

360406 With reference to magnetic dipole, match the terms of Column I with the items of Column II and choose the correct option from the codes given below.
Column I
Column II
A
Equatorial field for a short dipole
P
\(\frac{{{\mu _0}}}{{4\pi }}\frac{{2M}}{{{r^3}}}\)
B
Axial field for a short dipole
Q
\( - \overrightarrow M \cdot \vec B\)
C
Torque on a dipole
R
\(\overrightarrow M \times \vec B\)
D
Potential energy of a dipole
S
\(\frac{{{\mu _0}}}{{4\pi }}\frac{M}{{{r^3}}}\)

1 A-R, B-P, C-Q, D-S
2 A-S, B-P, C-R, D-Q
3 A-S, B-Q, C-R, D-P
4 A-Q, B-S, C-P, D-R
PHXII05:MAGNETISM and MATTER

360407 The magnetic moment of a bar magnet is \(0.5\,A{m^2}.\) It is suspended in a uniform magnetic field of \(8 \times {10^{ - 2}}\;T.\) The work done in rotating it from its most stable to most unstable position is

1 \(4 \times {10^{ - 2}}\;J\)
2 \(8 \times {10^{ - 2}}\;J\)
3 \(16 \times {10^{ - 2}}\;J\)
4 zero
PHXII05:MAGNETISM and MATTER

360408 The work done in turning a magnet of magnetic moment \(M\) by an angle of \(90^{\circ}\) from the meridian is \(n\) times the corresponding work done to turn it through an angle of \(60^{\circ}\) :

1 \(n=1 / 2\)
2 \(n=2\)
3 \(n=1 / 4\)
4 \(n=1\)
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PHXII05:MAGNETISM and MATTER

360405 A bar magnet of magnetic moment 2\(Am\) free to rotate about a vertical axis pass through its centre. The magnet is released from rest from east - west position. Then the \(K.E\) of the magnet as it takes north - south position is \(\left(B_{l I}=25 \mu T\right)\)

1 \(25\,\mu J\)
2 \(50\,\mu J\)
3 \(100\,\mu J\)
4 \(12.5\,\mu J\)
PHXII05:MAGNETISM and MATTER

360406 With reference to magnetic dipole, match the terms of Column I with the items of Column II and choose the correct option from the codes given below.
Column I
Column II
A
Equatorial field for a short dipole
P
\(\frac{{{\mu _0}}}{{4\pi }}\frac{{2M}}{{{r^3}}}\)
B
Axial field for a short dipole
Q
\( - \overrightarrow M \cdot \vec B\)
C
Torque on a dipole
R
\(\overrightarrow M \times \vec B\)
D
Potential energy of a dipole
S
\(\frac{{{\mu _0}}}{{4\pi }}\frac{M}{{{r^3}}}\)

1 A-R, B-P, C-Q, D-S
2 A-S, B-P, C-R, D-Q
3 A-S, B-Q, C-R, D-P
4 A-Q, B-S, C-P, D-R
PHXII05:MAGNETISM and MATTER

360407 The magnetic moment of a bar magnet is \(0.5\,A{m^2}.\) It is suspended in a uniform magnetic field of \(8 \times {10^{ - 2}}\;T.\) The work done in rotating it from its most stable to most unstable position is

1 \(4 \times {10^{ - 2}}\;J\)
2 \(8 \times {10^{ - 2}}\;J\)
3 \(16 \times {10^{ - 2}}\;J\)
4 zero
PHXII05:MAGNETISM and MATTER

360408 The work done in turning a magnet of magnetic moment \(M\) by an angle of \(90^{\circ}\) from the meridian is \(n\) times the corresponding work done to turn it through an angle of \(60^{\circ}\) :

1 \(n=1 / 2\)
2 \(n=2\)
3 \(n=1 / 4\)
4 \(n=1\)