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JEE Main 20137 April
Exam
JEE Main
Year
2013
Date
7 April
Subject
Physics
Chapter
Magnetic Properties of Matter

JEE Main 2013 · 7 April · Physics · Magnetic Properties of Matter

Two short bar magnets of length 1 cm each have magnetic moments 1...

Two short bar magnets of length 1cm1 cm each have magnetic moments 1.20Am21 .20 Am^{2} and 1.00Am21 .00 Am^{2} respectively. They are placed on a horizontal table parallel to each other with their N\text{N} poles pointing towards the south. They have a common magnetic equator and are separated by a distance of 20.0cm20 .0 cm. The value of the resultant horizontal magnetic induction at the mid-point O\text{O} of the line joining their centres is close to
( Horizontal component of earth's magnetic induction is 3.6×10−5Wbm−23 .6 \times {10}^{- 5}Wbm^{- 2} )Two short bar magnets of length 1 cm each have magnetic moments 1 .20 Am^ 2 and 1 .00 Am^ 2 respectively. They are

Options

  1. A3.50×10−4Wbm−23 .50 \times {10}^{- 4}Wb{m}^{- 2}
  2. B5.80×10−4Wbm−25 .80 \times {10}^{- 4}Wb{m}^{- 2}
  3. C3.6×10−5Wbm−23 .6 \times {10}^{- 5}Wb{m}^{- 2}
  4. D2.56×10−4Wbm−22 .56 \times {10}^{- 4}Wb{m}^{- 2}

Correct answer

D. 2.56×10−4Wbm−22 .56 \times {10}^{- 4}Wb{m}^{- 2}

Step-by-step solution

Two short bar magnets of length 1 cm each have magnetic moments 1 .20 Am^ 2 and 1 .00 Am^ 2 respectively. They are

Bnet=B1+B2+BH{\text{B}}_{\text{net}} = {\text{B}}_{1} + {\text{B}}_{2} + {\text{B}}_{H}

=μ04πM1x3+μ04πM2x3+BH= \dfrac{{\mu}_{0}}{4 \pi} \dfrac{{\text{M}}_{1}}{{\text{x}}^{3}} + \dfrac{{\mu}_{0}}{4 \pi} \dfrac{{\text{M}}_{2}}{{\text{x}}^{3}} + {\text{B}}_{\text{H}}

=10−7(1.2+1)(0.1)3+3.6×10−5= \dfrac{{ {10}^{- 7} ( 1.2 + 1 ) }}{{( 0.1 )}^{3}} + 3.6 \times {10}^{- 5}

=2.56×10−4Wb/m2= \text{2.56} \times {\text{10}}^{- 4} \text{Wb} / {\text{m}}^{2}
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