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Question

A regular polygon of 4 sides is formed by bending wires of total length 1 m which carries a current of 10 A. If the same polygon is reshaped into a circle with the same center then find the change in magnetic field at the center of the polygon O.


A
5.25 T
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B
5.25 μT
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C
5.25 nT
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D
5.25 mT
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Solution

The correct option is B 5.25 μT
Magnetic field of an n sided polygon is given by B1=μ0In2sin(πn)tan(πn)2π2rFrom the data given in the question, n=4 , r=12π m , I=10 A

B1=4π×107×10×(4)2×sin(π4)tan(π4)2×π2×12π

B1=640×107×sin(π4)tan(π4)

B1=642 μT or 45.25 μT

Now the wire is modified into a circle, circle has infinite number of sides. So,

Magnetic field at the center of circle is B2=μ0I2rThus, B2=4π×107×102×12π

B2=4π2 μT or 40 μT

Change in magnetic field at the center be B=|B1B2|=5.25 μT

Hence, option (b) is the correct answer.

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