Q114 / 125 · BITSAT 2010 · Physics

The magnetic field at the origin due to the current flowing in the wire is $-$ Figure

  • A
    $-\frac{\mu_{0} \mathrm{I}}{8 \pi \mathrm{a}}(\hat{\mathrm{i}}+\hat{\mathrm{k}})$
  • B
    $\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{a}}(\hat{\mathrm{i}}+\hat{\mathrm{k}})$
  • Correct answer
    C
    $\frac{\mu_{0} \mathrm{I}}{8 \pi \mathrm{a}}(-\hat{\mathrm{i}}+\hat{\mathrm{k}})$
  • D
    $\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{a} \sqrt{2}}(\hat{\mathrm{i}}-\hat{\mathrm{k}})$

Solution

$\mathrm{B}_{\mathrm{OD}}=0, \mathrm{~B}_{\mathrm{OB}}=0$ $\mathrm{~B}_{\mathrm{AB}}=\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{a} \sqrt{2}}\left[\cos 45^{\circ}(-\hat{\mathrm{i}})+\cos 45^{\circ} \hat{\mathrm{k}}\right]$ $=\frac{\mu_{0} \mathrm{I}}{8 \pi \mathrm{a}}(-\hat{\mathrm{i}}+\hat{\mathrm{k}})$

Hence, the correct answer is option: 'C'.

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