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Question

A circular loop of a wire and a long straight wire carry currents Ic and Il respectively as shown in figure. Assuming that these are palced in the same plane, the magnetic field will be zero at the centre O of the loop, when separation H is
1582166_4206577d048148dfb60c216d522f79a6.png

A
IlRIcπ
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B
IcRIlπ
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C
IcπIlR
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D
IlπIcR
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Solution

The correct option is A IlRIcπ
Given: A circular loop of a wire and a long straight wire carry currents Ic and Il respectively.
Solution: Magnetic field due to a circular loop at the
centre of the loop is
B1=μ04π2πIcR
Magnetic field due to a straight line at the
centre of the loop is
B2=μ02Il4πH
Both these fields act in opposite direction
hence total magnetic field at the centre of the
Ioop is

B=B1B2=μ02πIc4πRμ02Il4πH

B=0 (given).

μ02πIc4πR=μ02Il4πH or H=IlRIcπ
So,the correct option:A

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