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Question

A current of 1 A is flowing through the sides of an equilateral triangle with sides 4.5×102 m. Find the magnetic field at the center.

A
6×105 T
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B
2×105 T
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C
4×105 T
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D
43×105 T
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Solution

The correct option is C 4×105 T
An equilateral triangle ABC is given in the figure in which i current is flowing.
Given:
i=1 A; a=4.5×102 m

In triangle OQX,

tan60=QXOX

OX=QXtan60=a/23=a23

Let,
B1= magnetic field at O due to PQ
B2= magnetic field at O due to QR
B3= magnetic field at O due to RP

Now calculating magnetic field due to QR part at centre O,

B2=μ04πiOX[sinθ1+sinθ2]

B2=μ04π1(a/23)[sin60+sin60]

B2=μ04π23(4.5×102)×3=107×64.5×102

B2=43×105 T

Since triangle is equilateral, so all three sides create same magnetic field at the centre (direction will also be same),

B=B1+B2+B3=3B2

B=3×43×105=4×105 T

Hence, option (c) is correct.

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