JEE Main · 2013 · 07 Apr 2013 · Offline · Magnetic Properties of Matter

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

1.20 Am^{2}

and

1.00 Am^{2}

respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of 20.0 cm . The value of the resultant horizontal magnetic induction at the mid-point O of the line joining their centres is close to (Horizontal component of earth's magnetic induction is

3.6 \times 1 0^{- 5} Wb / m^{2}

)

(A) $2.56 \times 1 0^{- 4} Wb / m^{2}$ ✓ Correct
(B) $3.50 \times 1 0^{- 4} Wb / m^{2}$
(C) $5.80 \times 1 0^{- 4} Wb / m^{2}$
(D) $3.6 \times 1 0^{- 5} Wb / m^{2}$

Answer: (A)

Solution

Point O lies on the equatorial line of each short magnet, a distance

x = 0.10 m

from each, where a magnet of moment

M

produces

B = \frac{μ _{0}}{4 π} \frac{M}{x ^{3}}

. Arranged alike, the two equatorial fields add, and the earth's horizontal field adds on as well:

B = \frac{μ _{0}}{4 π} \frac{M _{1} + M _{2}}{x ^{3}} + B_{H} = \frac{1 0 ^{- 7} ( 2.2 )}{( 0.1 ) ^{3}} + 3.6 \times 1 0^{- 5} = 2.2 \times 1 0^{- 4} + 3.6 \times 1 0^{- 5} = 2.56 \times 1 0^{- 4} Wb/m^{2}

JEE Main · 2013 · 07 Apr 2013 · Offline · Single correct option

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JEE Main · 2013 · 07 Apr 2013 · Offline · Magnetic Properties of Matter

Solution

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