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SR EN 1504-2-2005
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50. If a bar magnet of magnetic moment 80 Am 2 and length length 16 cm is cut into 5 parts parallel parallel to length length and then 4 parts parallel to breadth, then (a the magnetic magnetic moment moment of each each part is 4 Am2 (b the length length of of each part part is 4 cm (c the pole pole strength strength of each part part is 100 Am. Am. 1. (a, (b and (c are true. 2. onl! (a and (b are true ". onl! (a and (c are true 4. onl! (b and (c are true 51. A bar magnet of magnetic moment # is bent in the form of a circle. $he ne% magnetic moment is &&&&&&& 1 # 2 2# " 'ero 4 #2 52. A bar magnet magnet of magnetic moment moment # is bent in the form of $he ne% magnetic moment is &&&&&&& #
1
such that all the parts are of e)ual length. length.
#
2
5
"
"
#
4
5
#
"
5". $hree identical bar magnets each of magnetic moment # are arranged in the form of an e)uilateral triangle such that at t%o *ertices li+e poles in contact. $he resultant magnetic moment is &&&&&&& 1 'ero 2 2# " # " 4 # 2 54. n- identical bar magnets of each magnetic moment # are arranged in the form a pol!gon such that the unli+e poles in contact. If one magnet is remo*ed and then replaced b! re*ersing the poles, then the resultant magnetic moment is &&&&&&& 1 #n 2 #n " 2# 4 "# 55. $he pole strength of a magnetic pole is n times the strength of another pole. If the force of repulsion bet%een them in air is %hen the! are at a distance d, then the strength of the %ea+er pole is &&&&&& 1
4π .d
2
2 n
µ o n
4π .d
2
"
µ o n
4π .d
2
2
4
µ o
4π .d n
µ o
56. An isolated north pole of mass 10 &" +g and pole strength 20 Am is +ept in a uniform magnetic field of induction 4 milli tesla. $he acceleration ac)uired b! the pole is &&& ms &2. 1 10 2 80 " 40 4 20 5/. $%o unli+e poles of same strength m are placed at the t%o corners of an e)uilateral triangle of side a. $he resultant magnetic induction at the third corner is &&& 1
"
µ o m 4π a
2
2
µ o m 4π a
2
"
2
µ o m 4π a
2
4 ero
58. A bar magnet is suspended at right angles to the direction of a uniform magnetic field. f ield. $he angle through %hich it should be rotated from this position so that the couple acting on it is half of the maimum couple is 1 "0o 2 60o " 45o 4 0o 5. A magnetic needle of pole strength 20 " Am is pi*oted at its center. Its north pole is pulled east%ard b! a string. $he tension re)uired to produce a deflection of "0 o from magnetic meridian (3 10&4 $ is &&&&& 1 4 10 &" 2 2 10 &" " 2 " 10&" 4 4 " 10&" 60. A bar magnet is suspended in the magnetic meridian %ith an unt%isted %ire. $he upper end of the %ir e is rotated through 180 o to deflect the magnet b! "0 o from magnetic meridian. 7hen this magnet is replaced b! another magnet, the upper end of the %ire is rotated through 2/0 o to deflect the magnet b! "0 o from magnetic meridian. $he ratio of the magnetic moments of the t%o magnets is 1 "94 2 192 " 49/ 4 598 61. $%o bar magnets of different lengths ha*e same magnetic moment. :n their aial lines at a distance d from their center 1 $he short short magne magnett produce producess stronger stronger field field.. 2 $he longe longerr magnet magnet produce producess stronger stronger field field.. " 3oth 3oth produ produce ce field field of of same same streng strength th 4 on one of of th these ese
62. $%o short bar magnets of each magnetic moment # are fastened at the center as sho%n in the figure. $he resultant magnetic induction at a point ; at distance d from the center of the combination is
<
;
< 1
µ o
2#
4π d
"
2
µ o
#
4π d
"
"
µ o
5#
4π
d
"
4 'ero
6". A short bar magnet of magnetic moment 1.6 Am 2 is placed %ith its ais in the magnetic meridian such that its south pole is facing to%ards geographic north. $he distance bet%een the t%o neutral points is &&& (3 4 10 &5 $ 1 20 cm 2 40 cm " 60 cm 4 80 cm 64. A *er! long bar magnet of pole strength 16 Am is placed *erticall! %ith its south pole on a table. $he distance of the neutral point from the table is &&&& (3 4 10 &5 $ 1 5 cm to%ards north 2 5 cm to%ards south " 20 cm to%ards north 4 20 cm to%ards south 65. $%o identical short bar magnets are arranged at the corners of a s)uare of side d as sho%n in the figure. $he resultant magnetic induction at point ; is ; <
1
µ o
2#
4π d
"
< 2
µ o
#
4π d
"
"
µ o
"#
4π d
"
4 ero
66. our magnets of e)ual length but magnetic moments #, 2#, "# and 4# are arranged in the form of a s)uare such that unli+e poles are in contact. $hen the resultant magnetic moment is 1 2 2 M 2 2 M " 10 # 4 2# 6/. A short bar magnet produces a deflection of "/ o in tanA position of deflection magnetometer %hen placed at a distance of 10 cm from the needle. At %hat distance from needle, the magnet be placed in tan 3 position to produce same deflection= 1 10 2 1" cm 2 5 22" cm " 5 cm 4 20 cm 68. $%o short bar magnets of same si'e %ith magnetic moments # 1 and #2 (#1>#2 are simultaneousl! used at the same position in a deflection magnetometer. 7hen the magnets are placed %ith li+e poles in contact the deflection is 60o and %hen unli+e poles are in contact the deflection is "0 o. $hen #1#2 1 " 2 6 " 4 4 2 6. A short bar magnet of magnetic moment # 1 produces a deflection "0 o %hen placed at some distance from the needle of a deflection magnetometer in tanA position. Another short bar magnet of magnetic moment #2 produces a deflection 60 o %hen placed at same distance from the needle in tan3 position. $hen #19#2 1 19" 2 "91 " 196 4 691 /0. A short bar magnet %hen placed at a distance of 8 cm in tanA position produces 60 o deflection. If the magnet is cut into " e)ual parts and one of them is +ept at the same distance in tanA position, the deflection is 1 "0o 2 60o " 45o 4 0o
/1. A bar magnet used in a *ibration magnetometer is heated so as to reduce its magnetic moment b! "6?. $he time period of the magnet (neglecting the changes in the dimensions of the magnet 1 increases b! "6? 2 decreases b! "6? " increases b! 25? 4 decreases b! 25? /2. $he magnetic needle of a *ibration magnetometer ma+es 12 oscillations per minute in the hori'ontal component of earth-s magnetic field. 7hen an eternal short bar magnet is placed at some distance along the ais of the needle in the same line it ma+es 15 oscillations per minute. If the poles of the bar are interchanged, the number of oscillations it ma+es per minute is 1 61 2 6" " 65 4 6/ /". A compass needle ma+es 10 oscillations per minute in the hori'ontal component of earth-s magnetic field. It ma+es 20 oscillations per minute %hen the field of a bar magnet supports the earth-s field. $he fre)uenc! of oscillation of the needle %hen the field of the bar magnet opposes the earth-s field is &&&&& oscillations per minute. 1 15 2 14.14 " 18 4 'ero /4. A short bar magnet %ith its north pole facing geographic north forms a neutral point at ; in the hori'ontal plane. If the magnet is rotated b! 0 o in the hori'ontal plane, the net magnetic induction at ; is (hori'ontal component of earth-s magnetic field 3 1 'ero
2 2 3
"
5 B H
4
2
5 B H
/5. A short magnet oscillates in a *ibration magnetometer %ith a time period of 0.1s %here the hori'ontal component of earth-s magnetic field is 24 µ$. An up%ard current of 18A is established in a *ertical %ire placed 20 cm east of the magnet. e% time period is 1 0.4s 2 0.2s " 0."s 4 0.1s /6. $he time period of oscillation of a bar magnet in earth-s magnetic field is $. 7hen another identical bar magnet is +ept on it at right angles to it such that their centers coincide, then the time period is 1 $ 2 212$ " 214$4 2$ //. $he time period of oscillation of a bar magnet in earth-s magnetic field is $. If it is cut into n identical parts parallel to its breadth and one part is used in oscillation magnetometer, then its time period is 1 $ 2 n$ " $n 4 n2$ /8. $he *ariation of the angular displacement %ith time of a bar magnet in a *ibration magnetometer is 2 d θ gi*en b! + 4θ = 0 . $he time period of the oscillation of the bar magnet is &&&& 2 dt
1 4s /. If A
4π d
2 1s
" 2s
4 ".14s
"
2 µ o
tan θ
,determined using deflection magnetometer %ith a short bar magnet at a distance d in 2
tanA position and 3
4π I
T
2
, determined using *ibration magnetometer %ith the same magnet (I is the
moment of inertia of the bar magnet, then (A3 12 gi*es &&&&& 1 magnetic moment of the magnet 2 hori'ontal component of earths field 2 length of the magnet 4 pole strength of the magnet 80. our li+e poles each of strength m are +ept at the four corners of a s)uare of side d. $he net magnetic force on the pole at an! corner is 1 'ero
