The Magnetic field dB of an element dl carries a steady current a
A. <span class="math-tex">\(\overrightarrow {dB} = \frac{{{\mu _o}}}{{4\pi }}i\left( {\frac{{\overrightarrow {dl} \times \vec r}}{r}} \right)\)</span>
B. <span class="math-tex">\(\overrightarrow {dB} = \frac{{{\mu _o}}}{{4\pi }}{i^2}\left( {\frac{{\overrightarrow {dl} \times \vec r}}{r}} \right)\)</span>
C. <span class="math-tex">\(\overrightarrow {dB} = \frac{{{\mu _o}}}{{4\pi }}{i^2}\left( {\frac{{\overrightarrow {dl} \times \vec r}}{{{r^2}}}} \right)\)</span>
D. <span class="math-tex">\(\overrightarrow {dB} = \frac{{{\mu _o}}}{{4\pi }}i\left( {\frac{{\overrightarrow {dl} \times \vec r}}{{{r^3}}}} \right)\)</span>
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Right Answer is: D
SOLUTION
CONCEPT:
Biot-Savart's Law:
- Biot-Savart’s law is used to determine the magnetic field at any point due to a current-carrying conductor.
- This law is although for infinitesimally small conductor yet it can be used for long conductors.
EXPLANATION:
- According to Biot-Savart Law, the magnetic field at point ‘ P ’ due to the current element \(i\overrightarrow {dl} \) is given by the expression,
\(\overrightarrow {dB} = \frac{{{\mu _o}}}{{4\pi }}i\left( {\frac{{\overrightarrow {dl} \times \vec r}}{{{r^3}}}} \right)\)
Where, μo = Absolute permeability of air or vacuum, \(i\overrightarrow {dl} \) = Current element and r = distance
