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When 2 Amp current is passed tarough a tangent galvanometer. It gives a deflection of $ 30 ^ \circ $ . For $ 60^ \circ $ deflaction, the current must be
$ I \;\alpha\; tan \phi $ $ { I_1 \over I_2 } = { tan \phi1 \over tan \phi 2 } $ $ { 2 \over I_2 } = { tan 30 ^\circ \over tan 60 ^\circ } $ $ I_2 = 6Amp $
The time period of a freely suspended magnet is a 4 seconds. If it is broken in length into two equal parts and one part is suspended in the same way, then its time period will be
$ \sqrt [2 \pi] { I \over MB_H} = 4 sec $ $ where I = { 1 \over 12 } ML^2 $ when magnet is cut into two equal havies, then new magnet moment M' = M/2 moment of inertia $ I' = 1/12 M' L'2 $ $ = { 1 \over 12 } \left({ M \over 2} \right) \left( { L \over 2 } \right)^2 $ $ = {1 \over 8 } . {1 \over 12} ML^2 $ $ I' = { I \over 8 } $ $ \therefore new time period T' = \sqrt [2 \pi] { I' \over M'BH} $ $ = \sqrt [ 2 \pi ] { { I \over 8 } \over \left( M \over 2 \right) BH} $ $ = {1 \over 2 } \sqrt [ 2 \pi ] { I \over MH } $ $ = { T \over 2 } $ $ = { 4 \over 2 } = 2 sec $
A thin magnetic needle oscillates in a horizontal plane with a period T. It is broken into nequal parts. The time period of each part will
Moment of inertio $ I = { mass \times (length)^2 \over 12 } $ $ \left ( \therefore I = { 1 \over 12} ML^2 \right) $ $ = { 1 \over n} \times \left( { 1 \over n} \right) ^2 $ $ = { 1 \over n^3 } time $ $ Magnetic moment M = pole strength \times length$ $ = { 1 \over n} time $ $ T = \sqrt [ 2 \pi ] { I \over MH } $ $ = \sqrt { {1 \over n^3 } \over {1 \over n} } time$ $ = {1 \over n } time $ $ \therefore T^1 = { T \over n} sec $
The plane of a dip circle is set in the geographic meridian and the apparent dip is $ \delta _1 $ . It is then set in a vertical plane per perpendicular to the geographic meridian. The appartent dip angle is $ \delta _2 $ . The declination at the place is
$ tan \delta_1 = { V \over Hcos \theta } $ $ tan \delta_2 = { V \over Hcos (90 ^\circ - \theta ) } = { V \over Hsin \theta } $ $ { tan \delta_1 \over tan \delta_2 } = { sin \theta \over cos \theta } $ ${ tan \delta_1 \over tan \delta_2 } = tan \theta $ $ \theta = tan^{-1} \left( tan \delta_1 \over tan \delta_2 \right) $
The coercivity of a bar magnet is 100 A/m. It is to be demagnetised byplacing it inside a solenoid of length 100 cm and number of turms 50. The current flowing through the solenoid will be
Coercivity H = 100 A/m ; l = 100 cm = 1m ; n =50 $ As H = nI \Rightarrow I = {H \over n} ={ 100 \over 50} = 2 Amp $
The angles of dip at two places are $30^\circ $ and $ 45 ^\circ $ . The ratio of horizontal components of earth's magnetic field at the two places will be
$ H_1 = B cos \delta_1 ; H_2 = B cos \delta_2 $ $ \therefore { H_1 \over H_2 } = { cos 30^ \circ \over cos 45^ \circ } $ $ = { \sqrt 3 \over \sqrt 2 } $
Read the assertion and reason carefully to mark the correct option out of the options given below. Assertion : We cannot think of magnetic field configuration with three poles. Reason : A bar magnet does exert a torque on itself due to its own field.
Read the assertion and reason carefully to mark the correct option out of the options given below. Assertion : If a compass needle be kept at magnetic north pole of the earth, the compass needle may stay in any direction. Reason : Dip needle will stay vertical at the north pole.
Read the assertion and reason carefully to mark the correct option out of the options given below. Assertion : Dia-magnetic materials can exhibit magnetism. Reason : Dia-magnetic materials have permanent magnetic dipole moment.
Diamagnetic materials do not have a permanent magnetic dipole moment; they are characterized by their ability to create an induced magnetic field in a direction opposite to an externally applied magnetic field. Therefore, the assertion is true (diamagnetic materials can exhibit magnetism in the presence of an external magnetic field), but the reason is false.
Read the assertion and reason carefully to mark the correct option out of the options given below. Assertion : A paramagnetic sample displays greater magnetisation when it is cooled. Reason : The magnetisaution does not depend on temperature.
For paramagnetic materials, the magnetization increases as the temperature decreases. This is because the thermal agitation of the atoms reduces, allowing the magnetic dipoles to align more easily with the external magnetic field. Hence, the assertion is true, but the reason is false since magnetization does depend on temperature.
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