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Dependence on Area and Orientation

The wire loop...

Question

The wire loop shown in figure carries a current as shown. The magnetic field at the centre O is:

zero

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\frac{μ_{0} i}{4} (\frac{1}{R_{1}} - \frac{1}{R_{2}})

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\frac{μ_{0} i}{4} (\frac{1}{R_{1}} + \frac{1}{R_{2}})

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\frac{μ_{0} i}{2} (\frac{1}{R_{1}} - \frac{1}{R_{2}})

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Solution

The correct option is B $\frac{μ_{0} i}{4} (\frac{1}{R_{1}} - \frac{1}{R_{2}})$
As shown in figure,the field due to smaller radius $R_{1}$ circular wire is outward but due to larger radius $R_{2}$ field is into the plane.
Now net field of 0 is $B$
$B = \frac{μ_{0} i}{4 R_{1}} - \frac{μ_{0} i}{4 R_{2}}$
$B = \frac{μ_{0} i}{4} (\frac{1}{R 1} - \frac{1}{R 2})$

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The wire loop shown in figure carries a current as shown. The magnetic field at the centre O is:

The correct option is B μ0i4(1R1−1R2)As shown in figure,the field due to smaller radius R1 circular wire is outward but due to larger radius R2 field is into the plane.Now net field of 0 is BB=μ0i4R1−μ0i4R2B=μ0i4(1R1−1R2)