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Question

A symmetric star shaped conducting wire loop is carrying a steady state current I as shown in the figure. The distance between the diametrically opposite vertices of the star is 4a. The magnitude of the magnetic field at the center of the loop is



A
3μ0I4πa[23]
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B
3μ0I2πa[31]
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C
3μ0I4πa[31]
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D
6μ0I4πa[3+1]
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Solution

The correct option is B 3μ0I2πa[31]

Magnitude of magnetic field at a particular distance d from a current carrying wire :-
BP=μ0I4πd[sinθ1sinθ2]
Magnitude of magnetic field at the centre due to wire AB :-
BCdue to AB=μ0I4πa[sin60sin30]
Net magnetic field due to star at the centre is equal to 12 times the magnetic field due to one section of star side.
BCnet =12BCdue to AB
=12×μ0I4πa[312]
=6μ0I4πa[31]=3μ0I2πa[31]

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